Peak sections and Bergman kernels on K\"ahler manifolds with complex hyperbolic cusps
Complex Variables
2024-01-05 v2 Differential Geometry
Abstract
By revisiting Tian's peak section method, we obtain a localization principle of the Bergman kernels on K\"ahler manifolds with complex hyperbolic cusps, which is a generalization of Auvray-Ma-Marinescu's localization result Bergman kernels on punctured Riemann surfaces [Auvray-Ma-Marinescu, Math. Ann., 2021]. Then we give some further estimates when the metric on the complex hyperbolic cusp is a K\"ahler-Einstein metric or when the manifold is a quotient of the complex ball. By applying our method directly to Poincar\'e type cusps, we also get a partial localization result.
Cite
@article{arxiv.2211.04091,
title = {Peak sections and Bergman kernels on K\"ahler manifolds with complex hyperbolic cusps},
author = {Shengxuan Zhou},
journal= {arXiv preprint arXiv:2211.04091},
year = {2024}
}
Comments
Revised version, to appear in "Mathematische Annalen."