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arXiv · 2607.04100

Fefferman-Szeg\H{o} kernels and finite-type rigidity on egg domains

Venkata Siddharth Pendyala
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Abstract

We compute the Fefferman boundary measure and the associated Fefferman--Szeg\H{o} kernel for the egg domains $$ E_{n,m}=\{(z,w)\in\mathbb{C}^{n-1}\times\mathbb{C}:\ |z|^2+|w|^{2m}<1\}. $$ The kernel is given both by an orthogonal monomial expansion and by a closed form in a natural auxiliary finite-type variable; its diagonal weak-boundary exponent recovers the integer $m$. For $n\ge2$, the associated Fefferman--Szeg\H{o} metric has constant scalar curvature only in the ball case $m=1$, and the K\"ahler--Einstein, constant Ricci-spectrum, and Bergman-proportionality statements follow as corollaries of the same calculation.

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Venkata Siddharth Pendyala. 2026-07-05. Fefferman-Szeg\H{o} kernels and finite-type rigidity on egg domains. https://arxiv.org/abs/2607.04100

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