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Articles de revues sur le sujet « Finsler norm »

Auteur : Grafiati

Publié le 2 juin 2025

Mis à jour le 31 juillet 2025

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1

Mönkkönen, Keijo. "Boundary rigidity for Randers metrics." Annales Fennici Mathematici 47, no. 1 (2021): 89–102. http://dx.doi.org/10.54330/afm.112492.

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 If a non-reversible Finsler norm is the sum of a reversible Finsler norm and a closed 1-form, then one can uniquely recover the 1-form up to potential fields from the boundary distance data. We also show a boundary rigidity result for Randers metrics where the reversible Finsler norm is induced by a Riemannian metric which is boundary rigid. Our theorems generalize Riemannian boundary rigidity results to some non-reversible Finsler manifolds. We provide an application to seismology where the seismic wave propagates in a moving medium.

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2

Akagi, Goro, Kazuhiro Ishige, and Ryuichi Sato. "The Cauchy problem for the Finsler heat equation." Advances in Calculus of Variations 13, no. 3 (2020): 257–78. http://dx.doi.org/10.1515/acv-2017-0048.

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AbstractLet H be a norm of {\mathbb{R}^{N}} and {H_{0}} the dual norm of H. Denote by {\Delta_{H}} the Finsler–Laplace operator defined by {\Delta_{H}u:=\operatorname{div}(H(\nabla u)\nabla_{\xi}H(\nabla u))}. In this paper we prove that the Finsler–Laplace operator {\Delta_{H}} acts as a linear operator to {H_{0}}-radially symmetric smooth functions. Furthermore, we obtain an optimal sufficient condition for the existence of the solution to the Cauchy problem for the Finsler heat equation\partial_{t}u=\Delta_{H}u,\quad x\in\mathbb{R}^{N},\,t>0,where {N\geq 1} and {\partial_{t}:=\frac{\part

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3

Ülgen, Semail, Esra Sengelen Sevim, and İrma Hacinliyan. "On Einstein Finsler metrics." International Journal of Mathematics 32, no. 09 (2021): 2150063. http://dx.doi.org/10.1142/s0129167x21500634.

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In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, a 1-form, and its norm and find equations with sufficient conditions for such Finsler metrics to become Ricci-flat. Using certain transformations, we show that these equations have solutions and lead to the construction of a large and special class of Einstein metrics.

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4

Shen, Zhongmin, and Changtao Yu. "On a class of Einstein Finsler metrics." International Journal of Mathematics 25, no. 04 (2014): 1450030. http://dx.doi.org/10.1142/s0129167x1450030x.

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In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, an 1-form, and its norm. We find equations which are sufficient conditions for such Finsler metrics to have constant Ricci curvature. Using certain transformations, we successfully solve these equations and hence construct a large class of Einstein metrics.

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Zamanzadeh, Seyyed Mohammad, Behzad Najafi, and Megerdich Toomanian. "On generalized P-reducible Finsler manifolds." Open Mathematics 16, no. 1 (2018): 718–23. http://dx.doi.org/10.1515/math-2018-0065.

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AbstractThe class of generalized P-reducible manifolds (briefly GP-reducible manifolds) was first introduced by Tayebi and his collaborates [1]. This class of Finsler manifolds contains the classes of P-reducible manifolds, C-reducible manifolds and Landsberg manifolds. We prove that every compact GP-reducible manifold with positive or negative character is a Randers manifold. The norm of Cartan torsion plays an important role for studying immersion theory in Finsler geometry. We find the relation between the norm of Cartan torsion, mean Cartan torsion, Landsberg and mean Landsberg curvatures

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Duy, Nguyen Tuan. "Some hardy type inequalities with finsler norms." Mathematica Slovaca 71, no. 2 (2021): 317–30. http://dx.doi.org/10.1515/ms-2017-0470.

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Rodrigues, Hugo Murilo, and Ryuichi Fukuoka. "Geodesic fields for Pontryagin type C⁰-Finsler manifolds." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 19. http://dx.doi.org/10.1051/cocv/2022013.

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Let M be a differentiable manifold, TxM be its tangent space at x ∈ M and TM = {(x, y);x ∈ M;y ∈ TxM} be its tangent bundle. A C0-Finsler structure is a continuous function F : TM → [0, ∞) such that F(x, ⋅) : TxM → [0, ∞) is an asymmetric norm. In this work we introduce the Pontryagin type C0-Finsler structures, which are structures that satisfy the minimum requirements of Pontryagin’s maximum principle for the problem of minimizing paths. We define the extended geodesic field ℰ on the slit cotangent bundle T*M\0 of (M, F), which is a generalization of the geodesic spray of Finsler geometry. W

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8

Chu, Cho-Ho. "Siegel domains over Finsler symmetric cones." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 778 (2021): 145–69. http://dx.doi.org/10.1515/crelle-2021-0027.

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Abstract Let Ω be a proper open cone in a real Banach space V. We show that the tube domain V ⊕ i ⁢ Ω {V\oplus i\Omega} over Ω is biholomorphic to a bounded symmetric domain if and only if Ω is a normal linearly homogeneous Finsler symmetric cone, which is equivalent to the condition that V is a unital JB-algebra in an equivalent norm and Ω is the interior of { v 2 : v ∈ V } {\{v^{2}:v\in V\}} .

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Lemmens, Bas. "Horofunction compactifications of symmetric cones under Finsler distances." Annales Fennici Mathematici 48, no. 2 (2023): 729–56. http://dx.doi.org/10.54330/afm.141190.

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In this paper we consider symmetric cones equipped with invariant Finsler distances, namely the Thompson distance and the Hilbert distance. We give a complete characterisation of the horofunctions of the symmetric cone \(A_+^\circ\) under the Thompson distance and establish a correspondence between the horofunction compactification of \(A_+^\circ\) and the horofunction compactification of the normed space in the tangent bundle. More precisely, we show that the exponential map extends as a homeomorphism between the horofunction compactification of the normed space in the tangent bundle, which i

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10

Shojaee, Neda, and Morteza Mirmohammad Rezaii. "Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure." Advances in Pure and Applied Mathematics 9, no. 2 (2018): 131–41. http://dx.doi.org/10.1515/apam-2016-0099.

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AbstractIn the present work, the harmonic vector field is defined on closed Finsler measure spaces through different approaches. At first, the weighted harmonic vector field is obtained as the solution space of a PDE system. Then a suitable Dirichlet energy functional is introduced. A σ-harmonic vector field is considered as the critical point of related action. It is proved that a σ-harmonic vector field on a closed Finsler space with an extra unit norm condition is an eigenvector of the defined Laplacian operator on vector fields. Moreover, we prove that a unit weighted harmonic vector field

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11

Eldeen Babiker, Saif, and Shawgy Hussein. "A Survey on Schwarz Lemma and Kobayashi Metrics for Harmonic and Holomorphic Functions." Journal of Research in Applied Mathematics 10, no. 10 (2024): 01–25. http://dx.doi.org/10.35629/0743-10100125.

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M. Mateljević [34] mainly consider various version of Schwarz lemma and its relatives related to harmonic and holomorphic functions including several variables. His methods (results) unify very recent approaches. This considerations include domains on which he can compute Kobayashi-Finsler norm. We intend do to a light application on the methods of [34].

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12

Atkin, C. J. "The Finsler geometry of groups of isometries of Hilbert Space." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 2 (1987): 196–222. http://dx.doi.org/10.1017/s1446788700028202.

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AbstractThe paper deals with six groups: the unitary, orthogonal, symplectic, Fredholm unitary, special Fredholm orthogonal, and Fredholm symplectic groups of an infinite-dimensional Hilbert space. When each is furnished with the invariant Finsler structure induced by the operator-norm on the Lie algebra, it is shown that, between any two points of the group, there exists a geodesic realising this distance (often, indeed, a unique geodesic), except in the full orthogonal group, in which there are pairs of points that cannot be joined by minimising geodesics, and also pairs that cannot even be

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13

Bellettini, Giovanni, and Ilaria Fragalà. "Elliptic approximations of prescribed mean curvature surfaces in Finsler geometry." Asymptotic Analysis 22, no. 2 (2000): 87–111. https://doi.org/10.3233/asy-2000-377.

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We approximate a hypersurface $\varSigma$ with prescribed anisotropic mean curvature with solutions $u _{\varepsilon}$ of suitable nonlinear elliptic equations depending on a small parameter $\varepsilon>0$ . We work in relative geometry, by endowing $\mathbb{R}^N$ with a Finsler norm $\phi$ describing the anisotropy. The main result states that $\varSigma$ and $\{u _{\varepsilon}=0\}$ are close of order $\varepsilon^2\vert\log\varepsilon\vert^2$ , and this estimate is optimal. This is obtained for two different elliptic equations by sub‐ and supersolutions technique, under smoothness and n

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14

ANDRUCHOW, ESTEBAN, and LÁZARO A. RECHT. "GEOMETRY OF UNITARIES IN A FINITE ALGEBRA: VARIATION FORMULAS AND CONVEXITY." International Journal of Mathematics 19, no. 10 (2008): 1223–46. http://dx.doi.org/10.1142/s0129167x08005102.

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Given a C*-algebra [Formula: see text] with trace τ, we compute the first and second variation formulas for the p-energy functional Fp of the unitary group [Formula: see text] of [Formula: see text], for p = 2n an even integer, namely: [Formula: see text] where [Formula: see text] is a smooth curve for t ∈ [a, b]. As an application of these formulas, we prove that if dp denotes the geodesic distance of the Finsler metric induced by the p-norm [Formula: see text] with [Formula: see text] and δ(t) is a geodesic of [Formula: see text] joining δ(0) = u0 and δ(1) = u1, then the mapping [Formula: se

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15

Liu, Yanjun. "Concentration-compactness principle of singular Trudinger–Moser inequality involving N-Finsler–Laplacian operator." International Journal of Mathematics 31, no. 11 (2020): 2050085. http://dx.doi.org/10.1142/s0129167x20500858.

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In this paper, suppose [Formula: see text] be a convex function of class [Formula: see text] which is even and positively homogeneous of degree 1. We establish the Lions type concentration-compactness principle of singular Trudinger–Moser Inequalities involving [Formula: see text]-Finsler–Laplacian operator. Let [Formula: see text] be a smooth bounded domain. [Formula: see text] be a sequence such that anisotropic Dirichlet norm[Formula: see text], [Formula: see text] weakly in [Formula: see text]. Denote [Formula: see text] Then we have [Formula: see text] where [Formula: see text], [Formula:

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16

CORACH, GUSTAVO, HORACIO PORTA, and LÁZARO RECHT. "GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS." International Journal of Mathematics 04, no. 02 (1993): 193–202. http://dx.doi.org/10.1142/s0129167x9300011x.

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The set A+ of positive invertible elements of a C*-algebra has a natural structure of reductive homogeneous manifold with a Finsler metric. Because pairs of points can be joined by uniquely determined geodesics and geodesics are "short" curves, there is a natural notion of convexity: C ⊂ A+ is convex if the geodesic segment joining a, b ∈ C is contained in C. We show that this notion is related to the classical convexity of real and operator valued functions. Several results about convexity are proved in this paper. The expressions of these results are closely related to the operator means of

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17

Berestovskii, V. N., and Yu G. Nikonorov. "The Chebyshev norm on the lie algebra of the motion group of a compact homogeneous Finsler manifold." Journal of Mathematical Sciences 161, no. 1 (2009): 97–121. http://dx.doi.org/10.1007/s10958-009-9538-4.

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18

Andruchow, Esteban, and Lázaro Recht. "Larotonda spaces: Homogeneous spaces and conditional expectations." International Journal of Mathematics 27, no. 02 (2016): 1650002. http://dx.doi.org/10.1142/s0129167x16500026.

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We define a Larotonda space as a quotient space [Formula: see text] of the unitary groups of [Formula: see text]-algebras [Formula: see text] with a faithful unital conditional expectation [Formula: see text] In particular, [Formula: see text] is complemented in [Formula: see text], a fact which implies that [Formula: see text] has [Formula: see text] differentiable structure, with the topology induced by the norm of [Formula: see text]. The conditional expectation also allows one to define a reductive structure (in particular, a linear connection) and a [Formula: see text]-invariant Finsler m

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19

Minculete, Nicuşor, Christian Pfeifer, and Nicoleta Voicu. "Inequalities from Lorentz-Finsler norms." Mathematical Inequalities & Applications, no. 2 (2021): 373–98. http://dx.doi.org/10.7153/mia-2021-24-26.

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20

Al-Rashed, Maryam H. A., and Bogusław Zegarliński. "Monotone norms and Finsler structures in noncommutative spaces." Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no. 04 (2014): 1450029. http://dx.doi.org/10.1142/s0219025714500295.

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21

Buzachero, L. F. S., E. Assunção, M. C. M. Teixeira, and E. R. P. da Silva. "Less Conservative Optimal Robust Control of a 3-DOF Helicopter." Journal of Control Science and Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/720203.

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This work proposes an improved technique for design and optimization of robust controllers norm for uncertain linear systems, with state feedback, including the possibility of time-varying the uncertainty. The synthesis techniques used are based on LMIs (linear matrix inequalities) formulated on the basis of Lyapunov’s stability theory, using Finsler’s lemma. The design has used the addition of the decay rate restriction, including a parameterγin the LMIs, responsible for decreasing the settling time of the feedback system. Qualitative and quantitative comparisons were made between methods of

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22

Li, Wenbai, Yu Xu, and Huaizhong Li. "Robustl2−l∞Filtering for Takagi-Sugeno Fuzzy Systems with Norm-Bounded Uncertainties." Discrete Dynamics in Nature and Society 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/979878.

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We study the filter design problem for Takagi-Sugeno fuzzy systems which are subject to norm-bounded uncertainties in each subsystem. As we know that the Takagi-Sugeno fuzzy linear systems can be used to represent smooth nonlinear systems, the studied plants can also be uncertain complex systems. We suppose to design a filter with the order of the original system which is also dependent on the normalized fuzzy-weighting function; that is, the filter is also a Takagi-Sugeno fuzzy filter. With the augmentation technique, an uncertain filtering error system can be obtained and the system matrices

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Salonen, Jannika, Susanna Slama, Anu Haavisto, and Johanna Rosenqvist. "A comparison of WPPSI-IV performance between Finland-Swedish minority children and the Scandinavian test norms: Findings from The FinSwed Study." Journal of the International Neuropsychological Society 29, no. 10 (2023): 943–52. http://dx.doi.org/10.1017/s1355617723000395.

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AbstractObjective:The Swedish Wechsler Preschool and Primary Scale of Intelligence (WPPSI-IV) is commonly used for assessing young children belonging to the Swedish-speaking minority in Finland (Finland-Swedes), but there is no information about the generalizability of this test and its norms to this minority. Cross-cultural comparisons of WPPSI-IV are also scarce. We compared the performance of Finland-Swedish children to the Scandinavian norms of the Swedish WPPSI-IV and explored the relationship between sociodemographic factors (age, sex, parental education level, bilingualism) and the perf

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Gresham, Gillian, Christie Y. Jeon, Dong Hee Kim, et al. "Abstract CT272: A cluster randomized trial to evaluate a church-based navigation model to increase breast cancer screening in Korean women (Faith In Action!): Trial in progress." Cancer Research 84, no. 7_Supplement (2024): CT272. http://dx.doi.org/10.1158/1538-7445.am2024-ct272.

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Abstract Background: Breast cancer is the most commonly diagnosed cancer among Korean American women and incidence in this group is rising. Advanced-stage disease is more frequent among Korean women diagnosed with breast cancer than in other ethnicities due to low adherence to screening. Lower socioeconomic status, cultural barriers, perceived norm, distrust of healthcare system, and lack of awareness and culturally tailored communication on benefits of screening contribute to low screening utilization. Church settings offer important platforms for education as a majority of Korean American wo

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Natesh, N., S. K. Narasimhamurthy та M. K. Roopa. "Conformal Vector Fields on Finsler Space with Special (α , β )- Metric". Journal of Advances in Mathematics and Computer Science, 29 березня 2019, 1–8. http://dx.doi.org/10.9734/jamcs/2019/v31i430117.

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In this paper, we study the conformal vector elds on a class of Finsler metrics. In particular Finsler space with special (α, β)- metric `F =\alpha +\frac{\beta^2}{\alpha} ` is dened in Riemannian metric α and 1-form β and its norm. Then we characterize the PDE's of conformal vector elds on Finsler space with special (α, β)- metric.

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Ilmavirta, Joonas, and Keijo Mönkkönen. "The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds." Journal of Geometric Analysis 33, no. 4 (2023). http://dx.doi.org/10.1007/s12220-022-01182-w.

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AbstractWe show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.

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Lemmens, Bas, and Kieran Power. "Horofunction Compactifications and Duality." Journal of Geometric Analysis 33, no. 5 (2023). http://dx.doi.org/10.1007/s12220-023-01205-0.

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AbstractWe study the global topology and geometry of the horofunction compactification of classes of symmetric spaces under Finsler distances in three settings: bounded symmetric domains of the form $$B=B_1\times \cdots \times B_r$$ B = B 1 × ⋯ × B r , where $$B_i$$ B i is an open Euclidean ball in $${\mathbb {C}}^{n_i}$$ C n i , with the Kobayashi distance, symmetric cones with the Hilbert distance, and Euclidean Jordan algebras with the spectral norm. For these spaces we show, that the horofunction compactification is naturally homeomorphic to the closed unit ball of the dual norm of the Fin

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Fărcăşeanu, Maria, Mihai Mihăilescu, and Denisa Stancu-Dumitru. "On a family of torsional creep problems in Finsler metrics." Canadian Journal of Mathematics, September 2, 2020, 1–18. http://dx.doi.org/10.4153/s0008414x20000681.

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Abstract The asymptotic behavior of solutions to a family of Dirichlet boundary value problems, involving differential operators in divergence form, on a domain equipped with a Finsler metric is investigated. Solutions are shown to converge uniformly to the distance function to the boundary of the domain, which takes into account the Finsler norm involved in the equation. This implies that a well-known result in the analysis of problems modeling torsional creep continues to hold in this more general setting.

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Farkas, Csaba, Alessio Fiscella, and Patrick Winkert. "Singular Finsler Double Phase Problems with Nonlinear Boundary Condition." Advanced Nonlinear Studies, September 3, 2021. http://dx.doi.org/10.1515/ans-2021-2143.

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Abstract In this paper, we study a singular Finsler double phase problem with a nonlinear boundary condition and perturbations that have a type of critical growth, even on the boundary. Based on variational methods in combination with truncation techniques, we prove the existence of at least one weak solution for this problem under very general assumptions. Even in the case when the Finsler manifold reduces to the Euclidean norm, our work is the first one dealing with a singular double phase problem and nonlinear boundary condition.

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Rovenski, V., and P. Walczak. "Deforming convex bodies in Minkowski geometry." International Journal of Mathematics 33, no. 01 (2021). http://dx.doi.org/10.1142/s0129167x22500033.

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We introduce and study certain deformation of Minkowski norms in [Formula: see text] determined by a set of [Formula: see text] linearly independent 1-forms and a smooth positive function of [Formula: see text] variables. In particular, the deformation of a Euclidean norm [Formula: see text] produces a Minkowski norm defined in our recent work; its indicatrix is a rotation hypersurface with a [Formula: see text]-dimensional axis passing through the origin. For [Formula: see text], our deformation generalizes the construction of [Formula: see text]-norms which form a rich class of “computable”

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Habibi, Sadaf, and Futoshi Takahashi. "Applications of p-harmonic transplantation for functional inequalities involving a Finsler norm." Partial Differential Equations and Applications 3, no. 3 (2022). http://dx.doi.org/10.1007/s42985-022-00168-1.

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Liu, Yanjun. "An Improved Trudinger–Moser Inequality Involving N-Finsler–Laplacian and Lp Norm." Potential Analysis, February 22, 2023. http://dx.doi.org/10.1007/s11118-023-10066-9.

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Esposito, Francesco, Luigi Montoro, Berardino Sciunzi, and Domenico Vuono. "Asymptotic behaviour of solutions to the anisotropic doubly critical equation." Calculus of Variations and Partial Differential Equations 63, no. 3 (2024). http://dx.doi.org/10.1007/s00526-024-02682-z.

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AbstractThe aim of this paper is to deal with the anisotropic doubly critical equation $$\begin{aligned} -\Delta _p^H u - \frac{\gamma }{[H^\circ (x)]^p} u^{p-1} = u^{p^*-1} \qquad \text {in } {\mathbb {R}}^N, \end{aligned}$$ - Δ p H u - γ [ H ∘ ( x ) ] p u p - 1 = u p ∗ - 1 in R N , where H is in some cases called Finsler norm, $$H^\circ $$ H ∘ is the dual norm, $$1<p<N$$ 1 < p < N , $$0 \le \gamma < \left( (N-p)/p\right) ^p$$ 0 ≤ γ < ( N - p ) / p p and $$p^*=Np/(N-p)$$ p ∗ = N p / ( N - p ) . In particular, we provide a complete asymptotic analysis of $$u \in \mathcal {D}^

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Caponio, Erasmo, Miguel Angel Javaloyes, and Antonio Masiello. "Multiple connecting geodesics of a Randers-Kropina metric via homotopy theory for solutions of an affine control system." Topological Methods in Nonlinear Analysis, February 26, 2023, 1–21. http://dx.doi.org/10.12775/tmna.2022.066.

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We consider a geodesic problem in a manifold endowed with a Randers-Kropina metric. This is a type of a singular Finsler metric arising both in the description of the lightlike vectors of a spacetime endowed with a causal Killing vector field and in the Zermelo's navigation problem with a wind represented by a vector field having norm not greater than one. By using Lusternik-Schnirelman theory, we prove existence of infinitely many geodesics between two given points when the manifold is not contractible. Due to the type of non-holonomic constraints that the velocity vectors must satisfy, this

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Vuono, Domenico. "Harnack inequalities for quasilinear anisotropic elliptic equations with a first order term." Nonlinear Differential Equations and Applications NoDEA 32, no. 4 (2025). https://doi.org/10.1007/s00030-025-01071-5.

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Abstract We consider weak solutions of the equation $$\begin{aligned} -\Delta _p^H u+a(x,u)H^q(\nabla u)=f(x,u) \quad \text {in } \Omega , \end{aligned}$$ - Δ p H u + a ( x , u ) H q ( ∇ u ) = f ( x , u ) in Ω , where H is in some cases called Finsler norm, $$\Omega $$ Ω is a domain of $${\mathbb {R}}^N$$ R N , $$p>1$$ p > 1 , $$q\ge \max \{p-1,1\}$$ q ≥ max { p - 1 , 1 } , and $$a(\cdot ,u)$$ a ( · , u ) , $$f(\cdot ,u)$$ f ( · , u ) are functions satisfying suitable assumptions. We exploit the Moser iteration technique to prove a Harnack type comparison inequality for solutions of the

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Pozuelo, Julián, та Manuel Ritoré. "Pansu–Wulff shapes in ℍ1". Advances in Calculus of Variations, 18 травня 2021. http://dx.doi.org/10.1515/acv-2020-0093.

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Abstract We consider an asymmetric left-invariant norm ∥ ⋅ ∥ K {\|\cdot\|_{K}} in the first Heisenberg group ℍ 1 {\mathbb{H}^{1}} induced by a convex body K ⊂ ℝ 2 {K\subset\mathbb{R}^{2}} containing the origin in its interior. Associated to ∥ ⋅ ∥ K {\|\cdot\|_{K}} there is a perimeter functional, that coincides with the classical sub-Riemannian perimeter in case K is the closed unit disk centered at the origin of ℝ 2 {{\mathbb{R}}^{2}} . Under the assumption that K has C 2 {C^{2}} boundary with strictly positive geodesic curvature we compute the first variation formula of perimeter for sets wi

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Morfe, Peter S., and Panagiotis E. Souganidis. "Comparison principles for second-order elliptic/parabolic equations with discontinuities in the gradient compatible with Finsler norms." Journal of Functional Analysis, April 2023, 109983. http://dx.doi.org/10.1016/j.jfa.2023.109983.

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Emmerson, Parker Yaohushuason. "Geometry of Phenomenological Velocity: Energy Numbers, Curvature and Fukaya-Type Categories." May 27, 2025. https://doi.org/10.5281/zenodo.15523017.

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Thank you, Yaohushua for letting me continue to distribute these mathematical gesturing forms so interesting. The paper constructs an algebraic–geometric framework around the “phenomenological ve-locity” expression v = pN/D that arose in previous informal work. We introduce (i) theenergy-number field E, (ii) a non-commutative velocity-string algebra V, (iii) a curvature scalarKPV defined from a “PV–Hessian”, and (iv) a curved A∞ category Fukv (M ) obtained from anordinary Fukaya category by multiplication with v. Basic structural results are proved; se

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