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## On isometries of the Kobayashi and Carathéodory metrics

### Tom 104 / 2012

Annales Polonici Mathematici 104 (2012), 121-151 MSC: Primary 32F45; Secondary 32Q45. DOI: 10.4064/ap104-2-2

#### Streszczenie

This article considers $C^1$-smooth isometries of the Kobayashi and Carathéodory metrics on domains in $\mathbb{C}^n$ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that $\mathbb{B}^n$ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of $C^0$-isometries $f : D_1 \rightarrow D_2$ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no $C^0$-isometry between a strongly pseudoconvex domain in $\mathbb{C}^2$ and certain classes of weakly pseudoconvex finite type domains in $\mathbb{C}^2$.

#### Autorzy

• Prachi MahajanDepartment of Mathematics
Indian Institute of Science
Bangalore 560 012, India
e-mail

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