平面凸体的Wulff曲率积分不等式

Integral inequality of Wulff curvature for plane convex bodies

本文主要研究平面上Wulff流情形下的Wulff曲率积分不等式。利用Green-Osher不等式和Wulff-Steiner多项式获得了对称与非对称凸体的任意次幂的Wulff曲率积分不等式。特别地,当其中一凸体为单位圆时,获得了平面凸曲线任意次幂的曲率积分不等式。

In this paper,we mainly study the integral inequality of Wulff curvature in the case of Wulff flow on the plane.By using Green-Osher inequality and Wulff-Steiner polynomials,we obtain the Wulff curvature integral inequality of any power of symmetric and nonsymmetric convex bodies.Specifically,when one of the convex bodies is an unit circle,the curvature integral inequality of any powers of the plane convex curve is obtained.