Remark About Heat Diffusion on Periodic Spaces

1997/07/18 by John Lott, Lott, John
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #advanced mathematical theories #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9707012

7 pages, AMS-Latex

arxiv created 1997/07/18 · openalex publication_date 1997/07/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a complete Riemannian manifold with a free cocompact Z^k-action. Let k(t,x,y) be the heat kernel on M. We compute the asymptotics of k(t,x,y) in the limit in which t goes to infinity and d(x,y) is comparable to sqrtt. We show that in this limit, the heat diffusion is governed by an effective Euclidean metric on R^k coming from the Hodge inner product on H¹(M/Z^k; R).

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