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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-2-2,
author = {Prachi Mahajan},
title = {On isometries of the Kobayashi and Carath\'eodory metrics},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {121-151},
zbl = {1244.32006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-2-2}
}
Prachi Mahajan. On isometries of the Kobayashi and Carathéodory metrics. Annales Polonici Mathematici, Tome 105 (2012) pp. 121-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-2-2/