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On the affine heat equation for non-convex curves |
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| Authors: | Sigurd Angenent Guillermo Sapiro Allen Tannenbaum |
| Institution: | Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 Guillermo Sapiro ; Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455 Allen Tannenbaum ; Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455 |
| 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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