Isoperimetric inequality for nearly spherical domains in the Bergman ball

David Kalaj

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arXiv · 2502.00891

Isoperimetric inequality for nearly spherical domains in the Bergman ball

David Kalaj

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Abstract

We prove a quantitative isoperimetric inequality for the nearly spherical subset of the Bergman ball in $\mathbb{C}^n$. We prove the Fuglede theorem for such sets. This result is a counterpart of a similar result obtained for the hyperbolic unit ball and it makes the first result on the isoperimetric phenomenon in the Bergman ball.

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David Kalaj. 2025-02-02. Isoperimetric inequality for nearly spherical domains in the Bergman ball. https://arxiv.org/abs/2502.00891

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