Harnack Inequality for f-Mean Curvature Flow

2025/11/28 by Li, Xiang-Dong, Yan, Qi
Mathematics · #53E10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2511.23330

openalex publication_date 2025/11/28 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a Li-Yau-Hamilton type Harnack estimate for the f-mean curvature flow in Euclidean space, which can be viewed as a gradient flow of the weighed area functional with the measure density function e^-f.

Citations

• Harnack estimate for mean curvature flow on the sphere
• Gaussian Mean curvature flow
• Comparison Geometry for the Bakry-Emery Ricci Tensor
• Long-time existence of mean curvature flow with external force fields

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