Robin heat kernel comparison on manifolds

TL;DR

This paper studies the Robin heat kernel on manifolds, establishing comparison theorems for heat kernels and eigenvalues, extending known results for Dirichlet and Neumann cases to Robin boundary conditions.

Contribution

It introduces new comparison theorems for Robin heat kernels and eigenvalues on manifolds and minimal submanifolds, generalizing previous Dirichlet and Neumann results.

Findings

Comparison theorems for Robin heat kernels on geodesic balls

Eigenvalue comparison for first Robin eigenvalues on minimal submanifolds

Extension of Dirichlet and Neumann results to Robin boundary conditions

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.