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Journal articles on the topic 'Geometry of metric spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

BOWDITCH, BRIAN H. "Median and injective metric spaces." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 1 (2018): 43–55. http://dx.doi.org/10.1017/s0305004118000555.

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AbstractWe describe a construction which associates to any median metric space a pseudometric satisfying the binary intersection property for closed balls. Under certain conditions, this implies that the resulting space is, in fact, an injective metric space, bilipschitz equivalent to the original metric. In the course of doing this, we derive a few other facts about median metrics, and the geometry of CAT(0) cube complexes. One motivation for the study of such metrics is that they arise as asymptotic cones of certain naturally occurring spaces.

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2

Kao, Lien-Yung. "Pressure type metrics on spaces of metric graphs." Geometriae Dedicata 187, no. 1 (2016): 151–77. http://dx.doi.org/10.1007/s10711-016-0194-9.

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3

Heydarpour, Majid. "On metric orbit spaces and metric dimension." Topology and its Applications 214 (December 2016): 94–99. http://dx.doi.org/10.1016/j.topol.2016.10.004.

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4

Guerrero Sánchez, David. "Domination by metric spaces." Topology and its Applications 160, no. 13 (2013): 1652–58. http://dx.doi.org/10.1016/j.topol.2013.06.014.

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5

Bayar, A., S. Ekmekçi, and Z. Akça. "On the Plane Geometry with Generalized Absolute Value Metric." Mathematical Problems in Engineering 2008 (2008): 1–8. http://dx.doi.org/10.1155/2008/673275.

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Metric spaces are among the most important widely studied topics in mathematics. In recent years, Mathematicians began to investigate using other metrics different from Euclidean metric. These metrics also find their place computer age in addition to their importance in geometry. In this paper, we consider the plane geometry with the generalized absolute value metric and define trigonometric functions and norm and then give a plane tiling example for engineers underlying Schwarz's inequality in this plane.

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6

Larotonda, Gabriel. "Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces." Forum Mathematicum 31, no. 6 (2019): 1567–605. http://dx.doi.org/10.1515/forum-2019-0127.

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AbstractWe study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic structure of homogeneous spaces M obtained by the quotient {M\simeq G/K}. Of particular interest are left-invariant metrics of G which are then bi-invariant for the action of K. We then focus on the geodesic structure of groups K that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all other short paths. We provide applications of the results obtained, in two settings: manifolds of Banach space linear operators, and groups of maps from compact manifolds.

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7

Tanaka, Yoshio. "Metrizability of decomposition spaces of metric spaces." Topology and its Applications 84, no. 1-3 (1998): 9–19. http://dx.doi.org/10.1016/s0166-8641(97)00078-3.

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8

Gaba, Yaé Ulrich, and Hans-Peter A. Künzi. "Partially ordered metric spaces produced by T0-quasi-metrics." Topology and its Applications 202 (April 2016): 366–83. http://dx.doi.org/10.1016/j.topol.2016.01.028.

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9

Megaritis, A. C. "τ-metrizable spaces". Applied General Topology 19, № 2 (2018): 253. http://dx.doi.org/10.4995/agt.2018.9009.

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<p>In [1], A. A. Borubaev introduced the concept of τ-metric space, where τ is an arbitrary cardinal number. The class of τ-metric spaces as τ runs through the cardinal numbers contains all ordinary metric spaces (for τ = 1) and thus these spaces are a generalization of metric spaces. In this paper the notion of τ-metrizable space is considered.</p>

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10

Schellekens, M. P. "Extendible spaces." Applied General Topology 3, no. 2 (2002): 169. http://dx.doi.org/10.4995/agt.2002.2061.

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<p>The domain theoretic notion of lifting allows one to extend a partial order in a trivial way by a minimum. In the context of Quantitative Domain Theory partial orders are represented as quasi-metric spaces. For such spaces, the notion of the extension by an extremal element turns out to be non trivial.</p><p>To some extent motivated by these considerations, we characterize the directed quasi-metric spaces extendible by an extremum. The class is shown to include the S-completable directef quasi-metric spaces. As an application of this result, we show that for the case of the invariant quasi-metric (semi)lattices, weightedness can be characterized by order convexity with the extension property.</p>

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11

Frenck, Georg, and Jan-Bernhard Kordaß. "Spaces of positive intermediate curvature metrics." Geometriae Dedicata 214, no. 1 (2021): 767–800. http://dx.doi.org/10.1007/s10711-021-00635-w.

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AbstractIn this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci curvature on a given high-dimensional $$\mathrm {Spin}$$ Spin -manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.

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12

DI CONCILIO, ANNA, and GIANGIACOMO GERLA. "Quasi-metric spaces and point-free geometry." Mathematical Structures in Computer Science 16, no. 01 (2006): 115. http://dx.doi.org/10.1017/s0960129506005111.

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13

Szydl/owski, Marek, Michael Heller, and Wiesl/aw Sasin. "Geometry of spaces with the Jacobi metric." Journal of Mathematical Physics 37, no. 1 (1996): 346–60. http://dx.doi.org/10.1063/1.531394.

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14

Granieri, Luca. "Metric Currents and Geometry of Wasserstein Spaces." Rendiconti del Seminario Matematico della Università di Padova 124 (2010): 91–125. http://dx.doi.org/10.4171/rsmup/124-6.

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15

Sturm, Karl-Theodor. "On the geometry of metric measure spaces." Acta Mathematica 196, no. 1 (2006): 65–131. http://dx.doi.org/10.1007/s11511-006-0002-8.

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16

GOLDFARB, BORIS, and JONATHAN L. GROSSMAN. "COARSE COHERENCE OF METRIC SPACES AND GROUPS AND ITS PERMANENCE PROPERTIES." Bulletin of the Australian Mathematical Society 98, no. 3 (2018): 422–33. http://dx.doi.org/10.1017/s0004972718000977.

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We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics, which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.

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17

Bazylevych, Lidia, Dušan Repovš, and Michael Zarichnyi. "Spaces of idempotent measures of compact metric spaces." Topology and its Applications 157, no. 1 (2010): 136–44. http://dx.doi.org/10.1016/j.topol.2009.04.040.

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18

Kushwaha, Ramdayal Singh, та Gauree Shanker. "On the ℒ-duality of a Finsler space with exponential metric αeβ/α". Acta Universitatis Sapientiae, Mathematica 10, № 1 (2018): 167–77. http://dx.doi.org/10.2478/ausm-2018-0014.

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Abstract The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

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19

CASE, JEFFREY S. "SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS." International Journal of Mathematics 23, no. 10 (2012): 1250110. http://dx.doi.org/10.1142/s0129167x12501108.

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Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Émery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.

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20

Foertsch, Thomas, and Viktor Schroeder>. "Products of Hyperbolic Metric Spaces." Geometriae Dedicata 102, no. 1 (2003): 197–212. http://dx.doi.org/10.1023/b:geom.0000006539.14783.aa.

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21

Antonyan, Natella, and Sergey A. Antonyan. "Universal metric proper G-spaces." Topology and its Applications 201 (March 2016): 388–402. http://dx.doi.org/10.1016/j.topol.2015.12.049.

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22

Hertel, Eike. "Convexity in finite metric spaces." Geometriae Dedicata 52, no. 3 (1994): 215–20. http://dx.doi.org/10.1007/bf01278473.

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23

Chugh, Renu, Tamanna Kadian, Anju Rani, and BE Rhoades. "Property in -Metric Spaces." Fixed Point Theory and Applications 2010, no. 1 (2010): 401684. http://dx.doi.org/10.1155/2010/401684.

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24

Ho, Pei-Ming. "Riemannian Geometry on Quantum Spaces." International Journal of Modern Physics A 12, no. 05 (1997): 923–43. http://dx.doi.org/10.1142/s0217751x97000694.

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An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space.

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25

Maeda, Yoshiaki, Steven Rosenberg, and Fabián Torres-Ardila. "The geometry of loop spaces I: Hs-Riemannian metrics." International Journal of Mathematics 26, no. 04 (2015): 1540002. http://dx.doi.org/10.1142/s0129167x15400029.

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A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms, which take values in pseudodifferential operators (ΨDOs). These calculations are used in the followup paper [10] to construct Chern–Simons classes on TLM which detect nontrivial elements in the diffeomorphism group of certain Sasakian 5-manifolds associated to Kähler surfaces.

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26

VEOMETT, E., and K. WILDRICK. "SPACES OF SMALL METRIC COTYPE." Journal of Topology and Analysis 02, no. 04 (2010): 581–97. http://dx.doi.org/10.1142/s1793525310000422.

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Mendel and Naor's definition of metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz is equivalent to an ultrametric space having infimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov–Hausdorff limits, and use these facts to establish a partial converse of the main result.

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27

Khalil, R., D. Hussein, and W. Amin. "Geometry of Modulus Spaces." gmj 9, no. 2 (2002): 295–301. http://dx.doi.org/10.1515/gmj.2002.295.

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Abstract Let ϕ be a modulus function, i.e., continuous strictly increasing function on [0, ∞), such that ϕ(0) = 0, ϕ(1) = 1, and ϕ(𝑥+𝑦) ≤ ϕ(𝑥)+ϕ(𝑦) for all 𝑥, 𝑦 in [0, ∞). It is the object of this paper to characterize, for any Banach space 𝑋, extreme points, exposed points, and smooth points of the unit ball of the metric linear space ℓ ϕ (𝑋), the space of all sequences (𝑥𝑛), 𝑥𝑛 ∈ 𝑋, 𝑛 = 1, 2, . . . , for which ∑ϕ(‖𝑥𝑛‖) < ∞. Further, extreme, exposed, and smooth points of the unit ball of the space of bounded linear operators on ℓ𝑝, 0 < 𝑝 < 1, are characterized.

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28

EASWARAMOORTHY, D., and R. UTHAYAKUMAR. "ANALYSIS ON FRACTALS IN FUZZY METRIC SPACES." Fractals 19, no. 03 (2011): 379–86. http://dx.doi.org/10.1142/s0218348x11005543.

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In this paper, we investigate the fractals generated by the iterated function system of fuzzy contractions in the fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard fuzzy metric spaces by using the fuzzy Banach contraction theorem. In addition to that, we discuss some results on fuzzy fractals such as Collage Theorem and Falling Leaves Theorem in the standard fuzzy metric spaces with respect to the standard Hausdorff fuzzy metrics.

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29

Nekvinda, Aleš, and Ondřej Zindulka. "Monotone Metric Spaces." Order 29, no. 3 (2011): 545–58. http://dx.doi.org/10.1007/s11083-011-9221-5.

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30

Çetkin, Vildan, Elif Güner, and Halis Aygün. "On 2S-metric spaces." Soft Computing 24, no. 17 (2020): 12731–42. http://dx.doi.org/10.1007/s00500-020-05134-w.

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31

Alenina, T. G. "Geometry of dual spaces of affine-metric connection." Journal of Mathematical Sciences 177, no. 4 (2011): 541–45. http://dx.doi.org/10.1007/s10958-011-0478-4.

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32

Heinonen, Juha, and Pekka Koskela. "Quasiconformal maps in metric spaces with controlled geometry." Acta Mathematica 181, no. 1 (1998): 1–61. http://dx.doi.org/10.1007/bf02392747.

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33

Selivanova, Svetlana. "Metric Geometry of Nonregular Weighted Carnot–Carathéodory Spaces." Journal of Dynamical and Control Systems 20, no. 1 (2013): 123–48. http://dx.doi.org/10.1007/s10883-013-9206-3.

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34

Sturm, Karl-Theodor. "On the geometry of metric measure spaces. II." Acta Mathematica 196, no. 1 (2006): 133–77. http://dx.doi.org/10.1007/s11511-006-0003-7.

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35

Good, Chris, and Sergio Macías. "Symmetric products of generalized metric spaces." Topology and its Applications 206 (June 2016): 93–114. http://dx.doi.org/10.1016/j.topol.2016.03.019.

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36

Artigue, Alfonso. "Generic dynamics on compact metric spaces." Topology and its Applications 255 (March 2019): 1–14. http://dx.doi.org/10.1016/j.topol.2018.12.007.

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37

Olela Otafudu, Olivier. "Gated sets in quasi-metric spaces." Topology and its Applications 263 (August 2019): 159–71. http://dx.doi.org/10.1016/j.topol.2019.05.026.

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38

Mineyev, Igor. "Flows and joins of metric spaces." Geometry & Topology 9, no. 1 (2005): 403–82. http://dx.doi.org/10.2140/gt.2005.9.403.

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39

Kapovich, Michael. "Triangle inequalities in path metric spaces." Geometry & Topology 11, no. 3 (2007): 1653–80. http://dx.doi.org/10.2140/gt.2007.11.1653.

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40

Mizokami, Takemi, and Fumio Suwada. "On resolutions of generalized metric spaces." Topology and its Applications 146-147 (January 2005): 539–45. http://dx.doi.org/10.1016/j.topol.2003.10.009.

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41

Gillam, W. D. "Embeddability properties of countable metric spaces." Topology and its Applications 148, no. 1-3 (2005): 63–82. http://dx.doi.org/10.1016/j.topol.2004.08.001.

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42

Romaguera, Salvador, and Michel Schellekens. "Partial metric monoids and semivaluation spaces." Topology and its Applications 153, no. 5-6 (2005): 948–62. http://dx.doi.org/10.1016/j.topol.2005.01.023.

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43

Shanker, Gauree, and Kirandeep Kaur. "Homogeneous Finsler spaces with exponential metric." Advances in Geometry 20, no. 3 (2020): 391–400. http://dx.doi.org/10.1515/advgeom-2020-0008.

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AbstractWe prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

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44

Chigogidze, Alex, and Vesko Valov. "Universal metric spaces and extension dimension." Topology and its Applications 113, no. 1-3 (2001): 23–27. http://dx.doi.org/10.1016/s0166-8641(00)00019-5.

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45

Mizokami, Takemi. "On hyperspaces of generalized metric spaces." Topology and its Applications 76, no. 2 (1997): 169–73. http://dx.doi.org/10.1016/s0166-8641(96)00112-5.

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46

Gregori, Valentín, Andrés López-Crevillén, Samuel Morillas, and Almanzor Sapena. "On convergence in fuzzy metric spaces." Topology and its Applications 156, no. 18 (2009): 3002–6. http://dx.doi.org/10.1016/j.topol.2008.12.043.

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47

Fedeli, Alessandro, and Attilio Le Donne. "On metric spaces and local extrema." Topology and its Applications 156, no. 13 (2009): 2196–99. http://dx.doi.org/10.1016/j.topol.2009.04.023.

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48

Liu, Chuan, and Shou Lin. "Generalized metric spaces with algebraic structures." Topology and its Applications 157, no. 12 (2010): 1966–74. http://dx.doi.org/10.1016/j.topol.2010.04.010.

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49

Antoniuk, Sylwia, and Paweł Waszkiewicz. "A duality of generalized metric spaces." Topology and its Applications 158, no. 17 (2011): 2371–81. http://dx.doi.org/10.1016/j.topol.2011.04.013.

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50

Mohamad, Abdul Adheem, and Tsukasa Yashiro. "TOPOLOGICAL STUDY OF GENERALIZED METRIC SPACES." JP Journal of Geometry and Topology 22, no. 2 (2019): 165–88. http://dx.doi.org/10.17654/gt022020165.

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