Yau's conjecture on smooth Reinhardt domains

Yuan Yuan

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arXiv · 2608.23089

Yau's conjecture on smooth Reinhardt domains

Yuan Yuan

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Abstract

We prove that a possibly unbounded Reinhardt domain in $\mathbb{C}^n$ with smooth boundary and a complete Bergman-Einstein metric is biholomorphic to the complex unit ball. In particular, no unbounded smooth Reinhardt domain admits a complete Bergman-Einstein metric.

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Yuan Yuan. 2026-08-24. Yau's conjecture on smooth Reinhardt domains. https://arxiv.org/abs/2608.23089

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