论文标题
通过曲率流量的惠特尼 - 浪漫源同属局部凸出曲线
Whitney-Graustein Homotopy of Locally Convex Curves via a Curvature Flow
论文作者
论文摘要
令$ x_0，\ wideTilde {x} $是两个平滑，闭合和本地凸出曲线，并具有相同的绕组编号。构建具有非局部术语的曲率流将$ x_0 $进化为$ \ widetilde {x} $。事实证明，该流量在全球范围内退出，保留了局部凸度和不断发展的曲线的弹性能量。如果两条曲线具有相同的弹性能，则曲率流将不断发展的曲线变形到目标曲线$ \ widetilde {x} $的时间趋于无穷大。
Let $X_0, \widetilde{X}$ be two smooth, closed and locally convex curves in the plane with same winding number. A curvature flow with a nonlocal term is constructed to evolve $X_0$ into $\widetilde{X}$. It is proved that this flow exits globally, preserves both the local convexity and the elastic energy of the evolving curve. If the two curves have same elastic energy then the curvature flow deforms the evolving curve into the target curve $\widetilde{X}$ as time tends to infinity.
