Remark About Heat Diffusion on Periodic Spaces

Details Remark About Heat Diffusion on Periodic Spaces Remark About Heat Diffusion on Periodic Spaces

1997-07-18

arxiv.org/abs/dg-ga/9707012v1

Mathematics

Differential Geometry

7 pages, AMS-Latex

Scientific paper

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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