论文标题
几乎是冬宫的几何形状中规定的高杜州标量曲率问题
The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry
论文作者
论文摘要
在本文中，我们考虑了几乎Hermitian流形上规定的Gauduchon标量曲率问题。通过在共形变化下推断高杜孔标量曲率的表达，该问题减小以求解具有指数非线性的半线性偏微分方程。使用超级和子解决方法，我们表明该半线性方程的解决方案的存在取决于与高久孔度相关的常数的符号。当符号为负时，我们给出了必要和充分的条件，即规定的函数是共形性遗传学度量的高杜孔标量曲率。此外，本文恢复了山贝的问题，开处方的雅马布问题和bismut yamabe问题。
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, the problem is reduced to solve a semi-linear partial differential equation with exponential nonlinearity. Using super and sub-solution method, we show that the existence of the solution to this semi-linear equation depends on the sign of a constant associated to Gauduchon degree. When the sign is negative, we give both necessary and sufficient conditions that a prescribed function is the Gauduchon scalar curvature of a conformal Hermitian metric. Besides, this paper recovers Chern Yamabe problem, prescribed Chern Yamabe problem and Bismut Yamabe problem.
