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The gradient flow for entropy on closed planar curves

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 نشر من قبل Glen Wheeler
 تاريخ النشر 2021
  مجال البحث
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In this paper we consider the steepest descent $L^2$-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 convex of class $C^2$ or embedded of class $W^{2,2}$ bounding a convex domain), the flow converges smoothly to a round expanding multiply-covered circle.



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