Isoperimetric Type Inequalities and Hypersurface Flows  

作　　者：Pengfei Guan Junfang Li 

机构地区：[1]Department of Mathematics and Statistics,McGill University,Montreal,Quebec H3A 0B9,Canada [2]Department of Mathematics,University of Alabama at Birmingham,Birmingham,Al 35294,USA

出　　处：《Journal of Mathematical Study》2021年第1期56-80,共25页数学研究（英文）

摘　　要：New types of hypersurface flows have been introduced recently with goals to establish isoperimetric type inequalities in geometry.These flows serve as efficient paths to achieve the optimal solutions to the problems of calculus of variations in geometric setting.The main idea is to use variational structures to develop hypersurface flows which are monotonic for the corresponding curvature integrals(including volume and surface area).These new geometric flows pose interesting but challenging PDE problems.Resolution of these problems have significant geometric implications.

关 键 词：Hypersurface curvature flows geometric inequalities quermassintegrals 

分 类 号：O18[理学—数学]