The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry  

作　　者：Yuxuan Li Wubin Zhou Xianchao Zhou 

机构地区：[1]School of Mathematical Sciences,Tongji University,Shanghai 200092,China [2]Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310023,China

出　　处：《Science China Mathematics》2024年第10期2357-2372,共16页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11701426);supported by National Natural Science Foundation of China(Grant No.11501505)。

摘　　要：In this paper,we consider the prescribed Gauduchon scalar curvature problem on almost Hermitian manifolds.By deducing the expression of the Gauduchon scalar curvature under the conformal variation,we reduce the problem to solving a semi-linear partial differential equation with exponential nonlinearity.Using the super-and sub-solutions method,we show that the existence of the solution to this semi-linear equation depends on the sign of a constant associated with the Gauduchon degree.When the sign is negative,we give both necessary and sufficient conditions such that a prescribed function is the Gauduchon scalar curvature of a conformal Hermitian metric.Besides,this paper recovers the Chern-Yamabe problem,the Lichnerowicz-Yamabe problem,and the Bismut-Yamabe problem.

关 键 词：almost Hermitian manifold Gauduchon connection prescribed scalar curvature problem 

分 类 号：O186.1[理学—数学]