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.
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The authors are very grateful to the unknown referees for helpful suggestions.
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This work was supported by the 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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Liu, H., Ma, L. On a Class of Generalized Curve Flows for Planar Convex Curves. Chin. Ann. Math. Ser. B 42, 367–382 (2021). https://doi.org/10.1007/s11401-021-0264-7
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DOI: https://doi.org/10.1007/s11401-021-0264-7