平面上保长度的闭凸曲线流及其应用

Closed-Convex Curve Flow with Length Preservation on the Plane and Its Application

摘要: 该文研究了平面上保长度的闭凸曲线流及其应用，在这篇文章中，给出了如果初始闭凸曲线是宽度的常宽曲线，那么在该流下发展曲线保持常宽，并且宽度与初始曲线宽度相等，并利用该曲线流证明平面上闭凸曲线的一个曲率倒数积分的几何不等式，对等号成立做了详细的几何分类解释。

Abstract: In this paper, the closed-convex curve flow with preserved length on the plane and its application are studied. If the initial closed-convex curve is a constant width curve of width, then the development curve remains constant width under the flow, and the width is equal to the width of the initial curve, and the curve flow is used to prove the geometric inequality of the reciprocal integral of a curvature of the closed convex curve on the plane, and the equivalence sign is established to explain the geometric classification in detail.