Gromov Hyperbolic Spaces and Applications to Complex Analysis
| Autor: | Hervé Pajot |
|---|---|
| Přispěvatelé: | Rolland, Ariane, Blanc-Centi, Léa, Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Mostow rigidity theorem
Pure mathematics Hyperbolic group media_common.quotation_subject Hyperbolic space 010102 general mathematics Mathematical analysis Gromov–Hausdorff convergence Hyperbolic manifold [MATH] Mathematics [math] Infinity 01 natural sciences Relatively hyperbolic group 0103 physical sciences Heisenberg group Mathematics::Metric Geometry 010307 mathematical physics 0101 mathematics [MATH]Mathematics [math] media_common Mathematics |
| Zdroj: | Metrical and Dynamical Aspects in Complex Analysis Blanc-Centi, Léa Metrical and Dynamical Aspects in Complex Analysis, 2195, Springer, pp.55-66, 2017, Lecture Notes in Mathematics, 978-3-319-65836-0 Lecture Notes in Mathematics ISBN: 9783319658360 |
| Popis: | International audience; The goal of this chapter is to explain some connections between hyperbolicity in the sense of Gromov and complex analysis/geometry. For this, we first give a short presentation of the theory of Gromov hyperbolic spaces and their boundaries. Then, we will see that the Heisenberg group can be seen as the boundary at infinity of the complex hyperbolic space. This fact will be used in Chap. 2 to give an idea of the proof of the celebrated Mostow rigidity Theorem in this setting. In the last section, we will explain why strongly pseudoconvex domains equipped with their Kobayashi distance are hyperbolic in the sense of Gromov. As an application of the general theory of Gromov hyperbolic spaces, we get a result about the extension of biholomorphic maps in this setting. Note that the case of the Gromov hyperbolicity of more general domains is discussed in Chap. 4. |
| Databáze: | OpenAIRE |
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