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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

On the affine heat equation
for non-convex curves


Authors: Sigurd Angenent, Guillermo Sapiro and Allen Tannenbaum
Journal: J. Amer. Math. Soc. 11 (1998), 601-634
MSC (1991): Primary 35K22, 53A15, 58G11
MathSciNet review: 1491538
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Abstract: 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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Additional Information

Sigurd Angenent
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Guillermo Sapiro
Affiliation: Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455

Allen Tannenbaum
Email: tannenba@ece.umn.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-98-00262-8
PII: S 0894-0347(98)00262-8
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.
Article copyright: © Copyright 1998 American Mathematical Society