Poisson equation on complete manifolds
Differential Geometry
2017-01-12 v1 Analysis of PDEs
Abstract
We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci curvature bounded below. As an application, we show that the curvature of a steady gradient Ricci soliton must decay exponentially if it decays faster than linear and the potential function is bounded above.
Cite
@article{arxiv.1701.02865,
title = {Poisson equation on complete manifolds},
author = {Ovidiu Munteanu and Chiung-Jue Anna Sung and Jiaping Wang},
journal= {arXiv preprint arXiv:1701.02865},
year = {2017}
}
Comments
44 pages