论文标题
Richberg的农业技术
The Richberg technique for subsolutions
论文作者
论文摘要
本说明使复杂的Richberg技术在多能理论中进行近似，以适应与一般的非线性凸式副本相关的$ f $ - 电势理论$ f \ subset j^2（x）$上的$ x $。主要定理是以下“本地与全局”结果。假设$ u $是一个连续的严格$ f $ -subharmonic函数，因此x $中的每个点$ x \具有一个基本的邻域系统，该域由$ c^\ infty $近似的“准”形式的域组成。然后，对于C（x）$中的任何正$ h \，存在严格的$ f $ -subharmonic函数$ w \ in C^\ infty（x）$，带有$ u <w <u+h $。应用程序包括$ {\ bf r}^n $上的所有凸常数系数替补，这是复杂且几乎复杂的歧管上的各种非线性替补，等等。
This note adapts the sophisticated Richberg technique for approximation in pluripotential theory to the $F$-potential theory associated to a general nonlinear convex subequation $F \subset J^2(X)$ on a manifold $X$. The main theorem is the following "local to global" result. Suppose $u$ is a continuous strictly $F$-subharmonic function such that each point $x\in X$ has a fundamental neighborhood system consisting of domains for which a "quasi" form of $C^\infty$ approximation holds. Then for any positive $h\in C(X)$ there exists a strictly $F$-subharmonic function $w\in C^\infty(X)$ with $u< w< u+h$. Applications include all convex constant coefficient subequations on ${\bf R}^n$, various nonlinear subequations on complex and almost complex manifolds, and many more.
