Heat content in non-compact Riemannian manifolds

2018/01/31 by M. van den Berg, Berg, Michiel van den · 1 citation
Mathematics · #35K20 #58J32 #58J35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1801.10539

openalex publication_date 2018/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω be an open set in a complete, smooth, non-compact, m-dimensional Riemannian manifold M without boundary, where M satisfies a two-sided Li-Yau gaussian heat kernel bound. It is shown that if Ω has infinite measure, and if Ω has finite heat content H_Ω(T) for some T>0, then H_Ω(t)0. Comparable two-sided bounds for H_Ω(t) are obtained for such Ω.

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