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A maximum principle for circle-valued temperatures

  • Andrew A. Cooper EMAIL logo
From the journal Advances in Geometry


In this note we prove a ‘maximum principle’ for circle-valued solutions of the (time-dependent) heat equation on closed Riemannian manifolds.

MSC 2010: 58C06; 58J35; 35B50
  1. Communicated by: S. Weintraub


The author thanks Vin de Silva and David Lipsky for helpful discussions on this topic, and the anonymous referee for simplifying a part of the proof of Theorem 10.


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Received: 2018-09-15
Revised: 2019-04-01
Published Online: 2019-09-11
Published in Print: 2021-01-27

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