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 $\mathrm {H}^1(M/\mathbb {Z}^k; \mathbb {R})$.References
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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