English

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}
}

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10 pages