Hilbert Geometry Without Convexity
| Autor: | Antonin Guilloux, E. Falbel, Pierre Will |
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| Přispěvatelé: | OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs (OURAGAN), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Generalization 010102 general mathematics Regular polygon 01 natural sciences Convexity Cantor set symbols.namesake Hilbert metric Differential geometry Fourier analysis [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 0103 physical sciences Metric (mathematics) symbols 010307 mathematical physics Geometry and Topology 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | The Journal of Geometric Analysis The Journal of Geometric Analysis, Springer, 2020, 30 (3), pp.2865-2896. ⟨10.1007/s12220-020-00426-x⟩ |
| ISSN: | 1050-6926 1559-002X |
| DOI: | 10.1007/s12220-020-00426-x⟩ |
| Popis: | The Hilbert metric on convex subsets of $${\mathbb {R}}^n$$ has proven a rich notion and has been extensively studied. We propose here a generalization of this metric to subsets of complex projective spaces (see also L. Dubois in J Lond Math Soc (2) 79(3):719–737, 2009) and give examples of geometric applications. Basic examples include the hyperbolic metric on complex hyperbolic spaces, the n-punctured spheres and $$\mathbb {RP}^1$$ minus a Cantor set. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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