球面上的平均场方程  

Mean Field Equation on Spheres

作　　者：桂长峰 胡烨耀 谢维洪 Gui Changfeng;Hu Yeyao;Xie Weihong(Department of Mathematics,The University of Texas at San Antonio,TX 78249,USA;School of Mathematics and Statistics,Central South University,Changsha 410075,China)

机构地区：[1]得克萨斯大学圣安东尼奥分校,圣安东尼奥78249 [2]中南大学数学与统计学院,长沙410075

出　　处：《数学理论与应用》2021年第3期13-37,共25页Mathematical Theory and Applications

摘　　要：本文介绍球面上平均场类方程的新进展及公开问题.特别地,我们引入一些新的Aubin-Onofri型不等式,同时讨论这些不等式与平均场类方程之间的紧密联系.In this expository note,we will introduce the recent progress and open problems concerning mean field type equations on spheres.In particular,some new inequalities of Aubin-Onofri type as well as their close connection to mean field type equations are presented.

关 键 词：平均场方程 Paneitz算子 共形度量 Szeg?极限定理 Moser-Trudinger不等式 

分 类 号：O175.2[理学—数学]