厦门大学学报（自然科学版）2023，Vol.62Issue(6)：912-923,12.DOI:10.6043/j.issn.0438-0479.202305012
微分几何中的几类曲率流的分析与应用
Analysis and application of curvature flow in differential geometry
摘要
Abstract
Geometric flows are regarded as important subjects in differential geometry and geometric analyses,which secure numerous applications in differential topology,functional analysis,partial differential equations,and general relativity among others.This paper is devoted to offering a survey on the developments of geometric flows based on works of the geometric-analysis group in Xiamen University.In the paper,we primarily discuss recent developments on the existence for complete noncompact Ricci flow,the existence for skew mean curvature flow,hypersurface curvature flow and geometric inequalities,as well as further open problems.关键词
几何流/完备非紧Ricci流/斜平均曲率流/超曲面曲率流/几何不等式Key words
geometric flow/complete noncompact Ricci flow/skew mean curvature flow/hypersurface curvature flow/geometric inequality分类
数理科学引用本文复制引用
贺飞,宋翀,夏超..微分几何中的几类曲率流的分析与应用[J].厦门大学学报（自然科学版）,2023,62(6):912-923,12.基金项目
国家自然科学基金(12141101,11971400,12271449,12126102) （12141101,11971400,12271449,12126102）
福建省自然科学基金(2021J06005) （2021J06005）
