On isometries of the Kobayashi and Carathéodory metrics

• Autorzy: Prachi Mahajan
• Języki publikacji: EN

Abstrakty

EN

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 a strongly pseudoconvex domain in ℂ² and certain classes of weakly pseudoconvex finite type domains in ℂ².

Kategorie tematyczne

• 32Q45: Hyperbolic and Kobayashi hyperbolic manifolds
• 32F45: Invariant metrics and pseudodistances

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 104
• Numer: 2
• Strony: 121-151

Daty

wydano

2012

Twórcy

autor

Prachi Mahajan

• Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India

Identyfikatory

DOI

10.4064/ap104-2-2