Quantitative upper bounds for Bergman kernels associated to smooth K\"ahler potentials
Complex Variables
2018-07-03 v1 Analysis of PDEs
Differential Geometry
Abstract
We give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the K\"ahler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.
Cite
@article{arxiv.1807.00204,
title = {Quantitative upper bounds for Bergman kernels associated to smooth K\"ahler potentials},
author = {Hamid Hezari and Hang Xu},
journal= {arXiv preprint arXiv:1807.00204},
year = {2018}
}
Comments
28 pages