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arXiv · 2412.03345

The K\"ahler-Ricci soliton on bounded pseudoconvex domains

Zehao Sha
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Abstract

In this paper, we study K\"ahler-Ricci solitons on bounded pseudoconvex domains in $\mathbb{C}^n$ with $C^2$ boundary. Under suitable assumptions, we prove that such solitons must be K\"ahler-Einstein. Building on Huang and Xiao's resolution of Cheng's conjecture, we further establish an analogous result for Bergman K\"ahler-Ricci solitons. Several model domains are presented to illustrate our results.

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Zehao Sha. 2024-12-04. The K\"ahler-Ricci soliton on bounded pseudoconvex domains. https://arxiv.org/abs/2412.03345

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