Abstract
AbstractIn this paper we consider the steepest descent $$L^2$$
L
2
-gradient flow of the entropy functional. The flow expands convex curves, with the radius of an initial circle growing like the square root of time. Our main result is that, for any initial curve (either immersed locally strictly convex of class $$C^2$$
C
2
or embedded of class $$W^{2,2}$$
W
2
,
2
bounding a strictly convex body), the flow converges smoothly to a round expanding multiply-covered circle.
Funder
Australian Research Council
Publisher
Springer Science and Business Media LLC
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