Sharp gradient estimates on weighted manifolds with compact boundary

2021/05/13 by Dung, Ha Tuan, Dung, Nguyen Thac, Wu, Jia-Yong
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.06185

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.

Related

• Some gradient estimates for nonlinear heat-type equations on smooth metric measure spaces with compact boundary
• Sharp gradient estimate and Yau's Liouville theorem for the heat equation on noncompact manifolds
• Sharp gradient estimate for heat kernels on RCD^*(K,N) metric measure spaces
• Sharp gradient estimates for a heat equation in Riemannian manifolds
• Gradient estimates of nonlinear equation on complete noncompact metric measure space with compact boundary