The Kähler-Ricci soliton on bounded pseudoconvex domains

2024/12/04 by Zehao Sha, Sha, Zehao · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2412.03345

Abstract

In this paper, we study Kähler-Ricci solitons on bounded pseudoconvex domains in ℂⁿ with C² boundary. Under suitable assumptions, we prove that such solitons must be Kähler-Einstein. Building on Huang and Xiao's resolution of Cheng's conjecture, we further establish an analogous result for Bergman Kähler-Ricci solitons. Several model domains are presented to illustrate our results.

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• On the Bergman metric of Cartan-Hartogs domains

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