Affiliation:
1. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China
Abstract
Let [Formula: see text] be a smooth n-dimensional Riemannian manifold for [Formula: see text]. Consider the conformal perturbation [Formula: see text] where [Formula: see text] is a smooth bounded positive function on [Formula: see text]. Denote by [Formula: see text] the Laplace–Beltrami operator of manifold [Formula: see text]. In this paper, we derive the upper bounds of the heat kernels for [Formula: see text] with [Formula: see text]. Moreover, we also investigate the gradient estimates of the heat kernel for [Formula: see text].
Funder
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation