On a Class of Generalized Curve Flows for Planar Convex Curves

Abstract

In this paper, the authors consider a class of generalized curve flow for convex curves in the plane. They show that either the maximal existence time of the flow is finite and the evolving curve collapses to a round point with the enclosed area of the evolving curve tending to zero, i.e., $\mathop {\lim}\limits_{t \to T} A(t) = 0$, or the maximal time is infinite, that is, the flow is a global one. In the case that the maximal existence time of the flow is finite, they also obtain a convergence theorem for rescaled curves at the maximal time.

Keywords

Curve flow / Convex curve / Longtime existence / Convergence

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