Remark About Heat Diffusion on Periodic Spaces
Abstract
Let M be a complete Riemannian manifold with a free cocompact Zk-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 Rk coming from the Hodge inner product on H1(M/Zk; R).
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