Exponential estimates for plurisubharmonic functions and stochastic dynamics

Kähler流形上的全阶指数混合：（拟）多次调和可观测函数

Exponential mixing of all orders on Kähler manifolds: (quasi-)plurisubharmonic observables

本文证明紧致Kähler流形上具有简单上同调作用的全纯自同构的最大熵测度对所有d.s.h.可观测函数具有全阶指数混合性，并由此推导出中心极限定理。

Equidistribution of non-pluripolar products associated with quasi-plurisubharmonic functions of finite energy

In this article, we consider currents given by the p-fold non-pluripolar product associated with a quasi-plurisubharmonic function of finite energy, and prove that normalized pull-backs of such currents converge to the Green (p, p)-current exponentially fast in the sense of currents for holomorphic endomorphisms of Pk.

Hénon-Sibony映射的混合性与中心极限定理：多次调和可观测函数

Mixing and CLT for Hénon-Sibony maps: plurisubharmonic observables

本文证明复Hénon映射及更一般的Hénon-Sibony映射的最大熵测度对多次调和可观测函数具有指数混合性和中心极限定理。

Relative types and extremal problems for plurisubharmonic functions

We study properties of relative types of plurisubharmonic functions with respect to maximal plurisubharmonic weights. It is shown that they give a general form for upper semicontinuous, tropically additive functionals on plurisubharmonic singularities. We consider some extremal problems whose solutions are Green-like functions that give best possible bounds on a plurisubharmonic function, given the values of its types relative to some of (or all) the weights. An analyticity theorem is proved for the upperlevel sets for the types with respect to exponentially Hölder continuous weights, which le…

Plurisubharmonic functions and real submanifolds of $\C^n$

We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold $M$. Applications are given to the Hausdorff measure of the intersection of the variety with $M$ and the exponential integrability of plurisubharmonic functions on $M$.

Estimates on Monge-Ampère operators derived from a local algebra inequality

The goal of this short note is to relate the integrability property of the exponential $e^{-2ϕ}$ of a plurisubharmonic function $ϕ$ with isolated or compactly supported singularities, to a priori bounds for the Monge-Ampère mass of $(dd^cϕ)^n$. The inequality is valid locally or globally on an arbitrary open subset $Ω$ in $\bC^n$. We show that $\int_Ω(ddϕ)^n<n^n$ implies $\int_Ke^{-2ϕ}<+\infty$ for every compact subset $K$ in $Ω$, while functions of the form $ϕ(z)=n\log|z-z_0|$, $z_0\inΩ$, appear as limit cases. The result is derived from an inequality of pure local algebra, which turns out a …