勒让德曲线的曲率型几何不等式

Curvature-Type Geometric Inequalities of Legendre Curves

本文主要研究勒让德曲线的曲率型几何不等式的两类加强形式,在Hausdorff距离和L2度量意义下,分别得到勒让德曲线的一个曲率型几何不等式的稳定性。此外,L2度量意义下的结果回答了Li和Wang提出的一个问题。

This article investigates two stronger versions of a curvature-type inequality of Legendre curves. With the help of the Hausdorff distance and the L2 metric, the stability of a curvature-type inequality of Legendre curves are concluded. Moreover, the result under the L2 metric gives a positive answer to the question appeared by Li and Wang.