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arXiv · 2410.14130

On the uniqueness of Poincaré type cscK metrics

Yulun Xu·Kai Zheng
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Abstract

Let $X$ be a compact Kähler manifold with a divisor $D$ which may have simple normal crossings. We prove that the $K$-energy is convex on the space of Poincaré type Kähler metrics. Then, we prove that the Poincaré type constant scalar curvature Kähler metric is unique up to an automorphism of $X$ preserving $D$.

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Yulun Xu, Kai Zheng. 2026-09-21. On the uniqueness of Poincaré type cscK metrics. https://arxiv.org/abs/2410.14130

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