Bessel Functions, Heat Kernel and the Conical K\"ahler-Ricci Flow
Differential Geometry
2013-05-02 v1
Abstract
Following Donaldson's oppenness theorem on deforming a conical K\"ahler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical K\"ahler-Ricci Flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber's formula on Bessel function of the second kind and Carslaw's heat kernel representation in \cite{Car}.
Keywords
Cite
@article{arxiv.1305.0255,
title = {Bessel Functions, Heat Kernel and the Conical K\"ahler-Ricci Flow},
author = {Xiuxiong Chen and Yuanqi Wang},
journal= {arXiv preprint arXiv:1305.0255},
year = {2013}
}
Comments
82 pages, 2 figures, comments are welcome