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Original Article

On the Convergence Rate of Bergman Metrics

Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
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Abstract

We study the convergence rate of Bergman metrics on the class of polarized pointed Kähler n-manifolds (M, L, g, x) with Vol(B1(x))>v and sec≤K on M. Relying on Tian’s peak section method (Tian in J Differ Geom 32(1):99–130, 1990), we show that the C1,α convergence of Bergman metrics is uniform. In the end, we discuss the sharpness of our estimates.

Keywords

Complex geometrySectional curvatureBergman metrics
Peking Mathematical Journal
Volume 7 Issue 1,
March 2024
Pages 399-439
DOI: 10.1007/s42543-022-00055-z
Cite this article:
Zhou, S. On the Convergence Rate of Bergman Metrics. Peking Math J 7, 399-439 (2024). https://doi.org/10.1007/s42543-022-00055-z

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Received: 07 March 2022
Revised: 06 August 2022
Accepted: 07 September 2022
Published: 26 December 2022
© Peking University 2022
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