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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Remark about heat diffusion on periodic spaces
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by John Lott PDF
Proc. Amer. Math. Soc. 127 (1999), 1243-1249 Request permission

Abstract:

Let $M$ be a complete Riemannian manifold with a free cocompact $\mathbb {Z}^k$-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 $\mathbb {R}^k$ coming from the Hodge inner product on $\mathrm {H}^1(M/\mathbb {Z}^k; \mathbb {R})$.
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Additional Information
  • John Lott
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
  • MR Author ID: 116090
  • ORCID: 0000-0002-5107-8719
  • Email: lott@math.lsa.umich.edu
  • Received by editor(s): August 5, 1997
  • Additional Notes: Research supported by NSF grant DMS-9704633.
  • Communicated by: Jozef Dodziuk
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 1243-1249
  • MSC (1991): Primary 58G11
  • DOI: https://doi.org/10.1090/S0002-9939-99-04685-7
  • MathSciNet review: 1476376