Remark About Heat Diffusion on Periodic Spaces
Abstract
Let M be a complete Riemannian manifold with a free cocompact Z^kaction. 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).
 Publication:

eprint arXiv:dgga/9707012
 Pub Date:
 July 1997
 DOI:
 10.48550/arXiv.dgga/9707012
 arXiv:
 arXiv:dgga/9707012
 Bibcode:
 1997dg.ga.....7012L
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 7 pages, AMSLatex