The Fefferman-Szegő metric on C^∞-smooth bounded strongly pseudoconvex domains in C^n has vanishing L2-Dolbeault cohomology outside middle degree, C^∞ bounded geometry, and yields rigidity results implying the domain is biholomorphic to the ball under gradient Kahler-Ricci soliton or constant scalar
The K\"ahler-Ricci soliton on bounded pseudoconvex domains
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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 2years
2026 2verdicts
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Explicit Fefferman-Szegő metric on egg domains D_{2m} is Kähler-Einstein and proportional to Bergman metric iff m=1.
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The Invariant Szeg\H{o} metric on strongly pseudoconvex domains
The Fefferman-Szegő metric on C^∞-smooth bounded strongly pseudoconvex domains in C^n has vanishing L2-Dolbeault cohomology outside middle degree, C^∞ bounded geometry, and yields rigidity results implying the domain is biholomorphic to the ball under gradient Kahler-Ricci soliton or constant scalar
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The invariant Szeg\H{o} metric on Egg domains
Explicit Fefferman-Szegő metric on egg domains D_{2m} is Kähler-Einstein and proportional to Bergman metric iff m=1.