On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 3, p. 393-417

Let Ω 1 and Ω 2 be strongly pseudoconvex domains in n and f:Ω 1 Ω 2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C 1 map to Ω ¯ 1 . We then prove that f| Ω 1 :Ω 1 Ω 2 is a CR or anti-CR diffeomorphism. It follows that Ω 1 and Ω 2 must be biholomorphic or anti-biholomorphic.

Classification:  32F45,  32Q45
@article{ASNSP_2006_5_5_3_393_0,
     author = {Seshadri, Harish},
     title = {On isometries of the carath\'eodory and Kobayashi metrics on strongly pseudoconvex domains},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
     number = {3},
     year = {2006},
     pages = {393-417},
     zbl = {1170.32309},
     mrnumber = {2274785},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0}
}
Seshadri, Harish. On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 3, pp. 393-417. http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0/

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