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Bibliografie tematiche / Convex projective geometry

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Articoli di riviste

Letteratura scientifica selezionata sul tema "Convex projective geometry"

Autore: Grafiati

Pubblicato: 16 novembre 2024

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Articoli di riviste sul tema "Convex projective geometry"

1

Wienhard, Anna, and Tengren Zhang. "Deforming convex real projective structures." Geometriae Dedicata 192, no. 1 (2017): 327–60. http://dx.doi.org/10.1007/s10711-017-0243-z.

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2

Weisman, Theodore. "Dynamical properties of convex cocompact actions in projective space." Journal of Topology 16, no. 3 (2023): 990–1047. http://dx.doi.org/10.1112/topo.12307.

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AbstractWe give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger–Guéritaud–Kassel: we show that convex cocompactness in is equivalent to an expansion property of the group about its limit set, occurring in different Grassmannians. As an application, we give a sufficient and necessary condition for convex cocompactness for groups that are hyperbolic relative to a collection of convex cocompact subgroups. We show that convex cocompactness in this situation is equivalent to the existence of an equivariant homeomorphism from the Bowditch boundary to the quotient of the limit set of the group by the limit sets of its peripheral subgroups.

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3

Kapovich, Michael. "Convex projective structures on Gromov–Thurston manifolds." Geometry & Topology 11, no. 3 (2007): 1777–830. http://dx.doi.org/10.2140/gt.2007.11.1777.

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4

Kim, Inkang. "Compactification of Strictly Convex Real Projective Structures." Geometriae Dedicata 113, no. 1 (2005): 185–95. http://dx.doi.org/10.1007/s10711-005-0550-7.

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5

Kohn, Kathlén, and Kristian Ranestad. "Projective Geometry of Wachspress Coordinates." Foundations of Computational Mathematics 20, no. 5 (2019): 1135–73. http://dx.doi.org/10.1007/s10208-019-09441-z.

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Abstract We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress (A rational finite element basis, Academic Press, New York, 1975). The defining polynomial of our adjoint hypersurface is the adjoint polynomial introduced by Warren (Adv Comput Math 6:97–108, 1996). This is a key ingredient for the definition of Wachspress coordinates, which are barycentric coordinates on an arbitrary convex polytope. The adjoint polynomial also appears both in algebraic statistics, when studying the moments of uniform probability distributions on polytopes, and in intersection theory, when computing Segre classes of monomial schemes. We describe the Wachspress map, the rational map defined by the Wachspress coordinates, and the Wachspress variety, the image of this map. The inverse of the Wachspress map is the projection from the linear span of the image of the adjoint hypersurface. To relate adjoints of polytopes to classical adjoints of divisors in algebraic geometry, we study irreducible hypersurfaces that have the same degree and multiplicity along the non-faces of a polytope as its defining hyperplane arrangement. We list all finitely many combinatorial types of polytopes in dimensions two and three for which such irreducible hypersurfaces exist. In the case of polygons, the general such curves are elliptic. In the three-dimensional case, the general such surfaces are either K3 or elliptic.

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6

Hildebrand, Roland. "Optimal Inequalities Between Distances in Convex Projective Domains." Journal of Geometric Analysis 31, no. 11 (2021): 11357–85. http://dx.doi.org/10.1007/s12220-021-00684-3.

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7

Benoist, Yves, and Dominique Hulin. "Cubic differentials and finite volume convex projective surfaces." Geometry & Topology 17, no. 1 (2013): 595–620. http://dx.doi.org/10.2140/gt.2013.17.595.

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8

Sioen, M., and S. Verwulgen. "Locally convex approach spaces." Applied General Topology 4, no. 2 (2003): 263. http://dx.doi.org/10.4995/agt.2003.2031.

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<p>We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [6]. We prove that the locally convex objects are exactly the ones generated (in the usual approach sense) by collections of seminorms. Furthermore, we construct a quantified version of the projective tensor product and show that the locally convex objects admitting a decent exponential law with respect to it are precisely the seminormed spaces.</p>

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9

Bray, Harrison, and David Constantine. "Entropy rigidity for finite volume strictly convex projective manifolds." Geometriae Dedicata 214, no. 1 (2021): 543–57. http://dx.doi.org/10.1007/s10711-021-00627-w.

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10

Zimmer, Andrew. "A higher-rank rigidity theorem for convex real projective manifolds." Geometry & Topology 27, no. 7 (2023): 2899–936. http://dx.doi.org/10.2140/gt.2023.27.2899.

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