Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition
Differential Geometry
2021-07-30 v2
Abstract
In this paper, on Riemannian manifolds with boundary, we establish a Yau type gradient estimate and Liouville theorem for harmonic functions under Dirichlet boundary condition. Under a similar setting, we also formulate a Souplet-Zhang type gradient estimate and Liouville theorem for ancient solutions to the heat equation.
Keywords
Cite
@article{arxiv.2012.09374,
title = {Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition},
author = {Keita Kunikawa and Yohei Sakurai},
journal= {arXiv preprint arXiv:2012.09374},
year = {2021}
}
Comments
10 pages