Conformal equivalence of visual metrics in pseudoconvex domains

  title={Conformal equivalence of visual metrics in pseudoconvex domains},
  author={Luca Capogna and Enrico Le Donne},
  journal={Mathematische Annalen},
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between bounded, smooth strongly pseudoconvex domains in $${\mathbb {C}}^n$$ C n are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth extensions of biholomorphic mappings between bounded smooth pseudoconvex domains. The proofs are inspired by Mostow’s proof of his rigidity theorem and… 

Homeomorphic extension of quasi-isometries for convex domains in $${\mathbb {C}}^d$$ C d and iteration theory

We study the homeomorphic extension of biholomorphisms between convex domains in $${\mathbb {C}}^d$$ C d without boundary regularity and boundedness assumptions. Our approach relies on methods from

Conformality and Q-harmonicity in sub-Riemannian manifolds

On the Gromov hyperbolicity of domains in ℂ n

— We present several recent results dealing with the metric properties of domains in the complex Euclidean space Cn. We provide with examples of domains, endowed with Finsler or Kähler metrics, that

Conformal and CR mappings on Carnot groups

We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR

Abstract Boundaries and Continuous Extension of Biholomorphisms

A BSTRACT . We present different constructions of abstract boundaries for bounded complete (Kobayashi) hyperbolic domains in C d , d ≥ 1 . These constructions essentially come from the geometric

Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance

We introduce the notion of locally visible and locally Gromov hyperbolic domains in C . We prove that a bounded domain in C is locally visible and locally Gromov hyperbolic if and only if it is



Geometric and analytic quasiconformality in metric measure spaces

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces,

Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains

Abstract. We give an estimate for the distance function related to the Kobayashi metric on a bounded strictly pseudoconvex domain with C2-smooth boundary. Our formula relates the distance function on

Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type

In this paper we prove necessary and sufficient conditions for the Kobayashi metric on a convex domain to be Gromov hyperbolic. In particular we show that for convex domains with $$C^\infty $$C∞

Conformality and Q-harmonicity in sub-Riemannian manifolds

Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains

  • Siqi Fu
  • Mathematics
    Canadian Mathematical Bulletin
  • 1995
Abstract In this paper we obtain the asymptotic expansions of the Carathéodory and Kobayashi metrics of strictly pseudoconvex domains with C∞ smooth boundaries in ℂn. The main result of this paper

Embeddings of Gromov hyperbolic spaces

Abstract. It is shown that a Gromov hyperbolic geodesic metric space X with bounded growth at some scale is roughly quasi-isometric to a convex subset of hyperbolic space. If one is allowed to

Uniformizing Gromov hyperbolic spaces

— The unit disk in the complex plane has two conformally related lives: one as an incomplete space with the metric inherited from R 2 , the other as a complete Riemannian 2-manifold of constant

Proper holomorphic mappings extend smoothly to the boundary

Kohn has proved that the Bergman projection associated to a smooth bounded domain D maps C°°(D) into C°°(D) when D is strictly pseudoconvex [11], and more generally, when the boundary of D satisfies

Metric Spaces of Non-Positive Curvature

This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by

Local boundary regularity of holomorphic mappings

Let f be a holomorphic mapping between two bounded domains D and D' in complex space ℂn. Suppose that D and D' contain smooth real hypersurfaces Γ and Γ′ as open subsets of their respective