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arXiv · 2408.09572

Local Rigidity of the Bergman Metric and of the K\"ahler Carath\'eodory Metric

Robert Xin Dong·Ruoyi Wang·Bun Wong
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Abstract

We prove that if the Carath\'eodory metric on a strictly pseudoconvex domain with a smooth boundary is locally K\"{a}hler near the boundary, then the domain is biholomorphic to a ball. We also establish a local rigidity theorem for domains with Bergman metrics of constant holomorphic sectional curvature, and highlight this relationship with the Lu constant.

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Robert Xin Dong, Ruoyi Wang, Bun Wong. 2024-08-18. Local Rigidity of the Bergman Metric and of the K\"ahler Carath\'eodory Metric. https://arxiv.org/abs/2408.09572

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