一类完全非线性流和均质积分不等式  

A fully-nonlinear flow and quermassintegral inequalities

作　　者：管鹏飞 李军方 

机构地区：[1]Department of Mathematics and Statistics, McGill University [2]Department of Mathematics, University of Alabama at Birmingham

出　　处：《中国科学：数学》2018年第1期147-156,共10页Scientia Sinica：Mathematica

摘　　要：本文对Euclid空间中的有界区域引进一类新的完全非线性曲率流并证明其存在及指数收敛性.沿该曲率流,本文将证明所有的均质积分(quermassintegral)都随时间单调变化,由此得以证明关于均质积分的一类Alexandrov-Fenchel不等式.We introduce a new type of fully-nonlinear curvature flow for bounded convex domains in Euclidean space and prove its longtime existence and exponential convergence. Along this flow, we will show all the quermassintegrals are monotonic which yields another proof of a class of Alexandrov-Fenchel inequalities of quermassintegrals via geometric flows.

关 键 词：完全非线性流 超曲面 几何不等式 星型区域 

分 类 号：O178[理学—数学]