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

· 2024 · math.CV · arXiv 2412.03345

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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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math.CV 1

years

2026 1

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UNVERDICTED 1

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  • The invariant Szeg\H{o} metric on Egg domains math.CV · 2026-06-23 · unverdicted · none · ref 29 · internal anchor

    Explicit Fefferman-Szegő metric on egg domains D_{2m} is Kähler-Einstein and proportional to Bergman metric iff m=1.