AN AREA-PRESERVING FLOW FOR CLOSED CONVEX PLANE CURVES

作者：Mao, Yueyue; Pan, Shengliang^*; Wang, Yiling

来源：International Journal of Mathematics, 2013, 24(4): 1350029.

DOI：10.1142/S0129167X13500298

• Closed convex plane curve
• area-preserving flow
• existence
• convergence

Motivated by Gage [On an area-preserving evolution equation for plane curves, in Nonlinear Problems in Geometry, ed. D. M. DeTurck, Contemporary Mathematics, Vol. 51 ( American Mathematical Society, Providence, RI, 1986), pp. 51-62] and Ma-Cheng [A non-local area preserving curve flow, preprint ( 2009), arXiv:0907.1430v2, [math.DG]], in this paper, an area-preserving flow for convex plane curves is presented. This flow will decrease the perimeter of the evolving curve and make the curve more and more circular during the evolution process. And finally, as t goes to infinity, the limiting curve will be a finite circle in the C-infinity metric.

• 出版日期2013-4
• 单位同济大学; 华东师范大学