Heat kernel coefficients on Kahler manifolds
Differential Geometry
2016-12-21 v3 High Energy Physics - Theory
Spectral Theory
Abstract
Polterovich proved a remarkable closed formula for heat kernel coefficients of the Laplace operator on compact Riemannian manifolds involving powers of Laplacians acting on the distance function. In the case of K\"ahler manifolds, we prove a combinatorial formula for powers of the complex Laplacian and use it to derive an explicit graph theoretic formula for the numerics in heat coefficients as a linear combination of metric jets based on Polterovich's formula.
Cite
@article{arxiv.1311.5510,
title = {Heat kernel coefficients on Kahler manifolds},
author = {Kefeng Liu and Hao Xu},
journal= {arXiv preprint arXiv:1311.5510},
year = {2016}
}
Comments
15 pages, substantially updated