Robin heat kernel comparison on manifolds

2022/08/29 by Xiaolong Li, Kui Wang, Li, Xiaolong +1 · 1 citation
Mathematics · Engineering · #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #3D Shape Modeling and Analysis

paper · pdf · doi:10.48550/arxiv.2208.13402

Abstract

We investigate the heat kernel with Robin boundary condition and prove comparison theorems for heat kernel on geodesic balls and on minimal submanifolds. We also prove an eigenvalue comparison theorem for the first Robin eigenvalues on minimal submanifolds. This generalizes corresponding results for the Dirichlet and Neumann heat kernels.

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• The Robin heat kernel and its expansion via Robin eigenfunctions

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