Sharp gradient estimates on weighted manifolds with compact boundary
Differential Geometry
2021-05-14 v1
Abstract
In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we prove Liouville theorems for ancient solutions satisfying the Dirichlet boundary condition and some sharp growth restriction near infinity. Our results can be regarded as a refinement of recent results due to Kunikawa and Sakurai.
Cite
@article{arxiv.2105.06185,
title = {Sharp gradient estimates on weighted manifolds with compact boundary},
author = {Ha Tuan Dung and Nguyen Thac Dung and Jia-Yong Wu},
journal= {arXiv preprint arXiv:2105.06185},
year = {2021}
}