Displaying similar documents to “Injective hyperbolicity of domains”

Hyperbolic-like manifolds, geometrical properties and holomorphic mappings

Grzegorz Boryczka, Luis Tovar (1996)

Banach Center Publications

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The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance ρ X α ( z 0 , z ) [ ] introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.

Concave domains with trivial biholomorphic invariants

Witold Jarnicki, Nikolai Nikolov (2002)

Annales Polonici Mathematici

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It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.

On isometries of the Kobayashi and Carathéodory metrics

Prachi Mahajan (2012)

Annales Polonici Mathematici

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This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between...