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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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On the affine heat equation for non-convex curves
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by Sigurd Angenent, Guillermo Sapiro and Allen Tannenbaum
J. Amer. Math. Soc. 11 (1998), 601-634


In this paper, we extend to the non-convex case the affine invariant geometric heat equation studied by Sapiro and Tannenbaum for convex plane curves. We prove that a smooth embedded plane curve will converge to a point when evolving according to this flow. This result extends the analogy between the affine heat equation and the well-known Euclidean geometric heat equation.
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Bibliographic Information
  • Sigurd Angenent
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 26245
  • ORCID: 0000-0003-3515-4539
  • Guillermo Sapiro
  • Affiliation: Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455
  • Allen Tannenbaum
  • Email:
  • Received by editor(s): April 24, 1997
  • Received by editor(s) in revised form: January 20, 1998
  • Additional Notes: This work was supported in part by grants from the National Science Foundation DMS-9058492, ECS-9122106, ECS-99700588, NSF-LIS, by the Air Force Office of Scientific Research AF/F49620-94-1-00S8DEF, AF/F49620-94-1-0461, AF/F49620-98-1-0168, by the Army Research Office DAAL03-92-G-0115, DAAH04-94-G-0054, DAAH04-93-G-0332, MURI Grant, Office of Naval Research ONR-N00014-97-1-0509, and by the Rothschild Foundation-Yad Hanadiv.
  • © Copyright 1998 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 11 (1998), 601-634
  • MSC (1991): Primary 35K22, 53A15, 58G11
  • DOI:
  • MathSciNet review: 1491538