On the Affine Heat Equation for Non-Convex Curves
Tannenbaum, Allen R.
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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.