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

DOI10.1090/proc/15768zbMath1493.53052arXiv2012.09374OpenAlexW3112358861WikidataQ115290691 ScholiaQ115290691MaRDI QIDQ5027219

Yohei Sakurai, Keita Kunikawa

Publication date: 4 February 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.09374

zbMATH Keywords

heat equationgradient estimateharmonic functionLiouville theorem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Heat equation (35K05) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (4)

Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition ⋮ Elliptic gradient estimates for a nonlinear equation with Dirichlet boundary condition ⋮ Liouville theorem for harmonic maps from Riemannian manifold with compact boundary ⋮ Triviality of bounded solutions and gradient estimates for nonlinear \(f\)-heat equations on complete smooth metric measure spaces

Cites Work

• Rigidity of manifolds with boundary under a lower Ricci curvature bound
• Volumes and limits of manifolds with Ricci curvature and mean curvature bounds
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary
• A matrix Harnack estimate for the heat equation
• Liouville theorem for heat equation Along ancient super Ricci flow via reduced geometry
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
• Geometric Analysis
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