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arXiv · 2608.08461

Isometries in the symmetrized bidisc, II

Armen Edigarian
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Abstract

We prove that every map $f:U\to\GG$ preserving the Poincar\'e distance and the Kobayashi distance is holomorphic or anti-holomorphic, where $U$ is a connected open subset of the unit disc. We also study the nonroyal automorphism orbits of $\GG$. A $C^1$ map on a connected relatively open part of such an orbit which preserves the restriction of the ambient Kobayashi--Royden metric is the restriction of a global automorphism or anti-automorphism of $\GG$. The same conclusion holds for maps preserving the ambient Kobayashi distance.

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Armen Edigarian. 2026-08-09. Isometries in the symmetrized bidisc, II. https://arxiv.org/abs/2608.08461

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