Pseudoconvexity and Gromov hyperbolicity |
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| Affiliation: | 1. Universität Bern, Mathematisches Institut, Sidlerstr. 5, 3012 Bern, Switzerland;2. Fachbereich Mathematik, MA 8-2, TU Berlin, Straβe des 17. Juni 136, 10623 Berlin, Germany;1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China;2. Department of Mathematics, Dingxi Teachers College, Dingxi 743000, China;1. Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA;2. Department of Mathematics, Bronx Community College of CUNY, Bronx, NY 10453, USA;3. Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, Jardim Botânico, CEP 22460-320, Rio de Janeiro, RJ, Brazil;4. Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Department of Mathematics, 6 Usacheva street, Moscow, Russia;1. Faculty of Mechanics and Mathematics of Moscow State University, Moscow 119991, Leninskie gory, MSU, Russian Federation;2. Russian Foreign Trade Academy, Moscow, Russian Federation |
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| Abstract: | We give an estimate for the distance functions related to the Bergman, Carathéodory, and Kobayashi metrics on a bounded strictly pseudoconvex domain with C2-smooth boundary. Our formula relates the distance function on the domain with the Carnot- Carathéodory metric on the boundary. As a corollary we conclude that the domain equipped with the any of the standard invariant distances is hyperbolic in the sense of Gromov. When the boundary of the domain is C3-smooth, our estimate is exact up to a fixed additive term. |
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