Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Remark about heat diffusion on periodic spaces

Author: John Lott
Journal: Proc. Amer. Math. Soc. 127 (1999), 1243-1249
MSC (1991): Primary 58G11
MathSciNet review: 1476376
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $M$ be a complete Riemannian manifold with a free cocompact ${\Bbb Z}^k$-action. Let $k(t, m_1, m_2)$ be the heat kernel on $M$. We compute the asymptotics of $k(t, m_1, m_2)$ in the limit in which $t \rightarrow \infty$ and $d(m_1, m_2) \sim \sqrt{t}$. We show that in this limit, the heat diffusion is governed by an effective Euclidean metric on ${\Bbb R}^k$ coming from the Hodge inner product on $\mathrm{H}^1(M/{\Bbb Z}^k; {\Bbb R})$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58G11

Retrieve articles in all journals with MSC (1991): 58G11

Additional Information

John Lott
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109

Received by editor(s): August 5, 1997
Additional Notes: Research supported by NSF grant DMS-9704633.
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 1999 American Mathematical Society