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

作　　者：贺飞 宋翀 夏超 HE Fei;SONG Chong;XIA Chao(School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2023年第6期912-923,共12页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(12141101,11971400,12271449,12126102);福建省自然科学基金(2021J06005)。

摘　　要：几何流是微分几何与几何分析研究的重要研究对象,同时几何流的研究在微分拓扑、泛函分析、偏微分方程、广义相对论等领域有诸多应用.本文对厦门大学几何分析研究团队近十年在几何流方面的研究进行综述,主要包括完备非紧Ricci流的存在性问题、斜平均曲率流的存在性问题、超曲面的曲率流与几何不等式等3个方面的研究成果及进一步的公开问题.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 

分 类 号：O186[理学—数学]