论文标题
到kähler歧管上的plurisubharmonic功能空间的几何形状
To the geometry of spaces of plurisubharmonic functions on a Kähler manifold
论文作者
论文摘要
考虑一个紧凑的Kähler歧管$（x，ω）$，以及$ω$的空间$ \ cal e（x，ω）= \ cal e $ - 完整的monge的plurisubharmonic函数 - 上面的pampèremase。我们引入了一个数量$ρ[u，v] $，以测量$ u，v \ in \ cal e $之间的距离； $ρ[u，v] $不是一个数字，而是在一定间隔$（0，v）\ subset \ mathbb r $上降低功能。我们探索$ρ[u，v] $的属性，使用它们，我们研究拉格朗日人和$ω$的相关能量空间 - plurisubharmonic函数。这里的许多结果概括了达瓦斯关于他的指标$d_χ$的发现。
Consider a compact Kähler manifold $(X,ω)$ and the space $\cal E(X,ω)=\cal E$ of $ω$--plurisubharmonic functions of full Monge--Ampère mass on it. We introduce a quantity $ρ[u,v]$ to measure the distance between $u, v\in\cal E$; $ρ[u,v]$ is not a number but rather a decreasing function on a certain interval $(0,V)\subset\mathbb R$. We explore properties of $ρ[u,v]$, and using them we study Lagrangians and associated energy spaces of $ω$--plurisubharmonic functions. Many results here generalize Darvas's findings about his metrics $d_χ$.
