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arXiv · 2504.08203

The uniqueness of Poincar\'e type extremal K\"ahler metric

Yulun Xu
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Abstract

Let $D$ be a smooth divisor on a closed K\"ahler manifold $X$. Suppose that $Aut_0(D)=\{Id\}$. We prove that the Poincar\'e type extremal K\"ahler metric with a cusp singularity at $D$ is unique up to a holomorphic transformation on $X$ that preserves $D$. This generalizes Berman-Berndtson's work on the uniqueness of extremal K\"ahler metrics from closed manifolds to some complete and noncompact manifolds.

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Yulun Xu. 2025-04-11. The uniqueness of Poincar\'e type extremal K\"ahler metric. https://arxiv.org/abs/2504.08203

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