Isoperimetric inequality for nearly spherical domains in the Bergman ball in ℂⁿ

2025/02/02 by Kalaj, David
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.00891

Abstract

We prove a quantitative isoperimetric inequality for the nearly spherical subset of the Bergman ball in ℂⁿ. 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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