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arXiv · 2611.09341

Period bounds for Bergman kernel variation and the Suita defect

Fusheng Deng·Gang Huang·Kefeng Liu
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Abstract

The periods of holomorphic differentials give an explicit lower bound for the curvature of Bergman evaluation matrices. We prove this bound along the Green sublevels of a smooth plane domain. For scalar evaluation at the Green pole, equality at one regular level holds precisely when that sublevel is simply connected. For complete jets at the Green pole, the matrices have continuous first derivatives, including at critical levels, and their logarithmic determinant defects are integrals of nonnegative curvature densities. A further estimate bounds the accumulated period energy by the determinant defect, with a constant independent of the jet order. On a multiply connected domain, all these defects vanish up to the first critical Green value and become strictly positive above it.

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Fusheng Deng, Gang Huang, Kefeng Liu. 2026-11-06. Period bounds for Bergman kernel variation and the Suita defect. https://arxiv.org/abs/2611.09341

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