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| On a Class of Generalized Curve Flows for Planar Convex Curves* |
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Citation： |
Huaqiao LIU,Li MA.On a Class of Generalized Curve Flows for Planar Convex Curves*[J].Chinese Annals of Mathematics B,2021,42(3):367~382 |
| Page view： 489
Net amount： 450 |
Authors： |
Huaqiao LIU; Li MA |
Foundation： |
Key Project Foundation of Henan Province (No.18A110014), the National Natural Science Foundation of China (No.11771124) and a Research Grant from USTB, China. |
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| 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., limt→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 |
Classification： |
53A04, 35A15, 35K15, 35K55 |
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