曲线流在平面曲线的几个不等式中的应用

Applications of Curve Flows to Inequalities on Plane Curves

通过建立平面中的曲线收缩流的单调公式,给出三个几何不等式新的证明.特别地,通过经典曲线收缩流给出了R^(2)上Ros定理一个新的证明,通过一种保面积的曲线收缩流分别给出了R^(2)上Ros定理以及其加强形式和曲线的熵不等式新的证明.

In this paper,by establishing new monotone formulas along the shortening flows for plane curves,we present new proofs for three geometric inequalities.In particular,a new proof of the Ros theorem on R^(2)is given by the classical curve shortening flow.And new proofs of the Ros theorem on R^(2)and its refined form and an entropy inequality for plane curve are given by an area-preserving curve shortening flow.