On isometries of the Kobayashi and Carathéodory metrics

Prachi Mahajan. "On isometries of the Kobayashi and Carathéodory metrics." Annales Polonici Mathematici 104.2 (2012): 121-151. <http://eudml.org/doc/280954>.

@article{PrachiMahajan2012,
abstract = {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.},
author = {Prachi Mahajan},
journal = {Annales Polonici Mathematici},
keywords = {Kobayashi metric; Caratheodory metric; Kobayashi distance; Caratheodory distance; points of finite type},
language = {eng},
number = {2},
pages = {121-151},
title = {On isometries of the Kobayashi and Carathéodory metrics},
url = {http://eudml.org/doc/280954},
volume = {104},
year = {2012},
}

TY - JOUR
AU - Prachi Mahajan
TI - On isometries of the Kobayashi and Carathéodory metrics
JO - Annales Polonici Mathematici
PY - 2012
VL - 104
IS - 2
SP - 121
EP - 151
AB - 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.
LA - eng
KW - Kobayashi metric; Caratheodory metric; Kobayashi distance; Caratheodory distance; points of finite type
UR - http://eudml.org/doc/280954
ER -