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Remark About Heat Diffusion on Periodic Spaces

John Lott
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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 sqrt{t}. 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 H^1(M/Z^k; R).

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John Lott. 1997-07-18. Remark About Heat Diffusion on Periodic Spaces. https://arxiv.org/abs/dg-ga/9707012

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