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arXiv · 2012.09374

Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition

Keita Kunikawa·Yohei Sakurai
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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.

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Keita Kunikawa, Yohei Sakurai. 2020-12-17. Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition. https://arxiv.org/abs/2012.09374

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