On the Affine Heat Equation for Non-Convex Curves

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1853/32428

Title: On the Affine Heat Equation for Non-Convex Curves
Author: Angenent, Sigurd ; Sapiro, Guillermo ; Tannenbaum, Allen R.
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.
Description: ©1998 American Mathematical Society. First published in Journal of the American Mathematical Society, Vol. 11, No. 3, July 1998; published by the American Mathematical Society. DOI: 10.1090/S0894-0347-98-00262-8
Type: Article
URI: http://hdl.handle.net/1853/32428
Citation: Sigurd Angenent, Guillermo Sapiro, and Allen Tannenbaum, "On the Affine Heat Equation for Non-Convex Curves," Journal of the American Mathematical Society, Vol. 11, No. 3, July 1998, 601-634.
Date: 1998-07
Contributor: University of Minnesota. Dept. of Electrical and Computer Engineering
University of Wisconsin--Madison. Dept. of Mathematics
Publisher: Georgia Institute of Technology
American Mathematical Society
Subject: Partial differential equations
Affine differential geometry
Parabolic equations and systems
Analysis on manifolds

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