Remark About Heat Diffusion on Periodic Spaces
dg-ga
2008-02-03 v1 Differential Geometry
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).
Cite
@article{arxiv.dg-ga/9707012,
title = {Remark About Heat Diffusion on Periodic Spaces},
author = {John Lott},
journal= {arXiv preprint arXiv:dg-ga/9707012},
year = {2008}
}
Comments
7 pages, AMS-Latex