论文标题
$ω$ - plurisubharmonic函数的强拓扑
The strong topology of $ω$-plurisubharmonic functions
论文作者
论文摘要
在$（x，ω）$compactKähler歧管上，给定PSH（x，ω）$（即奇异类型）中的模型类型$ψ\，我们证明了Monge-ampère操作员是$ψ$固定的有限能量的$ n Morge-ampère操作员是同型$ - $ - $ - $ - $ - $ - $ψ弱拓扑的改进，使相对能量变得连续。此外，给定一个完全有序的家庭$ \ MATHCAL {A} $的模型类型包络，具有正质量的正质量代表不同的奇点类型，该集合$ x _ {\ Mathcal {a}}，y _ _ {\ Mathcal {a}} $分别给出了所有$ coultial unitial unitial unitial unitial unitial unite unite unite unite unite unite $ψ$ψ在\ edline {\ Mathcal {a}} $中变化$ψ\具有两个天然强的拓扑结构，可扩展工会每个组成部分的强拓扑。我们表明，Monge-ampère操作员在$ x _ {\ Mathcal {a}} $和$ y _ {\ Mathcal {a}} $之间产生同构。作为一个应用，我们还证明，当措施具有均匀的$ l^{p} $ - 以$ p> 1 $均匀的有限密度，并且规定的奇异点完全订购时，我们还证明了一系列规定的复杂Monge-ampère方程解决方案的稳定稳定性。
On $(X,ω)$ compact Kähler manifold, given a model type envelope $ψ\in PSH(X,ω)$ (i.e. a singularity type) we prove that the Monge-Ampère operator is an homeomorphism between the set of $ψ$-relative finite energy potentials and the set of $ψ$-relative energy measures endowed with their strong topologies given as the coarsest refinements of the weak topologies such that the relative energies become continuous. Moreover, given a totally ordered family $\mathcal{A}$ of model type envelopes with positive total mass representing different singularities types, the sets $X_{\mathcal{A}}, Y_{\mathcal{A}}$ given respectively as the union of all $ψ$-relative finite energy potentials and of all $ψ$-relative finite energy measures varying $ψ\in\overline{\mathcal{A}}$ have two natural strong topologies which extends the strong topologies on each component of the unions. We show that the Monge-Ampère operator produces an homeomorphism between $X_{\mathcal{A}}$ and $Y_{\mathcal{A}}$. As an application we also prove the strong stability of a sequence of solutions of prescribed complex Monge-Ampère equations when the measures have uniformly $L^{p}$-bounded densities for $p>1$ and the prescribed singularities are totally ordered.
