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arXiv 2412.033452024-12math.CVmath.DG

在有界伪凸域上的Kähler-Ricci孤立子

The Kähler-Ricci soliton on bounded pseudoconvex domains

Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）

Zehao Sha

备注：: 19 pages. More details added

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AI总结：

本文研究有界伪凸域中C²边界上的Kähler-Ricci孤立子，证明其必为Kähler-爱因斯坦度量，并基于Huang和Xiao对Cheng猜想的解决，进一步建立Bergman Kähler-Ricci孤立子的类似结果。

摘要：

在本文中，我们研究有界伪凸域在C^n中的Kähler-Ricci孤立子，其边界为C²。在合适的假设下，我们证明此类孤立子必为Kähler-爱因斯坦度量。基于Huang和Xiao解决Cheng猜想的结果，我们进一步建立了Bergman Kähler-Ricci孤立子的类似结果。几个模型域被提出以说明我们的结果。

英文摘要：

In this paper, we study Kähler-Ricci solitons on bounded pseudoconvex domains in $\mathbb{C}^n$ with $C^2$ 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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