On the Gromov hyperbolicity of domains in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℂ</mml:mi> <mml:mi>n</mml:mi> </mml:msup></mml:math>

Hervé Gaussier

Type: Article

Publication Date: 2021-04-21

Citations: 1

DOI: https://doi.org/10.5802/tsg.362

Abstract

We present several recent results dealing with the metric properties of domains in the complex Euclidean space C n .We provide with examples of domains, endowed with Finsler or Kähler metrics, that are (or are not) Gromov hyperbolic.We also present how different notions, such as the Gromov hyperbolicity, the holomorphic bisectional curvature or the d'Angelo type may be related for smooth bounded domains in C n .We also present several open questions in the core of the paper.

Locations

Séminaire de théorie spectrale et géométrie - View - PDF

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Works Cited by This (30)

Action	Title	Year	Authors
+ PDF Chat	Finite type conditions for real hypersurfaces	1979	John P. D’Angelo
+	Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. I.	1933	Stefan Bergmann
+ PDF Chat	Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains	2000	Zoltán M. Balogh Mario Bonk
+ PDF Chat	Real hypersurfaces in complex manifolds	1974	Shiing-Shen Chern Jürgen Moser
+	Hyperbolic Complex Spaces	1998	Shôshichi Kobayashi
+ PDF Chat	Inequality between the Bergman metric and Carathéodory differential metric	1978	Kyong T. Hahn
+	On Kähler manifolds with negative holomorphic bisectional curvature	1976	Paul Yang
+	On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation	1980	Shiu‐Yuen Cheng Shing‐Tung Yau
+ PDF Chat	Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains	2010	Peter Hästö Ana Portilla José M. Rodrı́guez Eva Tourı́s
+	The Poincaré Metric of Plane Domains	1978	Alan F. Beardon Ch. Pommerenke