Heat kernel estimates on manifolds with ends with mixed boundary condition

2021/08/12 by Emily Dautenhahn, Dautenhahn, Emily, Laurent Saloff‐Coste +1
Computer Science · Mathematics · #31B05 (Secondary) #58J35 #58J65 #60J65 (Primary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2108.05790

openalex publication_date 2021/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and Saloff-Coste by allowing for Dirichlet boundary condition. The proof requires the construction of a global harmonic function which is then used in the h-transform technique.

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