A Kobayashi metric version of Bun Wong's theorem

TL;DR

This paper proves that strongly pseudoconvex domains with noncompact Kobayashi isometry groups are biholomorphic to the unit ball, extending Bun Wong's theorem using Kobayashi metrics.

Contribution

It introduces a Kobayashi metric version of Bun Wong's theorem, characterizing domains with large automorphism groups.

Findings

Strong pseudoconvex domains with noncompact isometry groups are biholomorphic to the unit ball.

The result extends classical automorphism group characterizations using Kobayashi metrics.

Provides new insights into the geometry of complex domains and their automorphism groups.

Abstract

We prove that a strongly pseudoconvex domain with noncompact group of Kobayashi/Royden metric isometries must be biholomorphic to the unit ball.