Related papers: Indicators for Plurisubharmonic Functions of Logar…
We study the masses charged by $(dd^cu)^n$ at isolated singularity points of plurisubharmonic functions $u$. It is done by means of the local indicators of plurisubharmonic functions. As a consequence, bounds for the masses are obtained in…
Monge-Ampere currents generated by plurisubharmonic functions of logarithmic growth are studied. Upper bounds for their total masses are obtained in terms of growth characteristics of the functions. In particular, this gives a…
A notion of local indicator for a plurisubharmonic function is introduced. The indicator is a certain plurisubharmonic function in the unit polydisc, which controls the behavior of the considered function near a fixed point of its…
The paper considers a global version of the notion of log canonical threshold for plurisubharmonic functions $u$ of logarithmic growth in $\mathbb{C}^n$, aiming at description of the range of all $p>0$ such that $e^{-u}\in…
In this paper we derive formulas for the Monge-Amp\`ere measures of functions of the form $\log|\Phi|_c$, where $\Phi$ is a holomorphic map on a complex manifold $X$ of dimension $n$ with values in $\mathbb{C}^{n+1}\setminus\{0\}$ and…
We study a Monge-Amp\`ere type equation in the class of $p$-plurisubharmonic functions and establish first and second order interior estimates. As an application of these we show that $p$-plurisubharmonic functions with constant operator…
Let $u$ and $v$ be two plurisubharmonic functions in the domain of definition of the Monge-Amp\`ere operator on a domain $\Omega\subset {\bf C}^n$. We prove that if $u=v$ on a plurifinely open set $U\subset \Omega$ that is Borel measurable,…
We will define the Monge-Amp\`ere operator on finite (weakly) plurifinely plurisubharmonic functions in plurifinely open sets in complex n-space and show that it defines a positive measure. Ingredients of the proof include a direct proof…
We study the projective logarithmic potential $\mathbb{G}_{\mu}$ of a Probability measure $\mu$ on the complex projective space $\mathbb{P}^{n}$. We prove that the Range of the operator $\mu\longrightarrow \mathbb{G}_{\mu}$ is contained in…
Let $F$ be a polynomial endomorphism of $\C^n$ which extends holomorphically to $\P^n$. We prove that the dimension of $\mu_F$, the pluriharmonic measure on the boundary of the filled Julia set of $F$, is bounded above by $2n-1$.
Answering a question of A.Zygmund in \cite{MR} G.MacLane and L.Rubel described boundedness of $L_2$-norm w.r.t. the argument of $\log |B|$, where $B$ is a Blaschke product. We generalize their results in several directions. We describe…
In this paper we are concerned with the problem of local and global subextensions of (quasi-)plurisubharmonic functions from a "regular" subdomain of a compact K\"ahler manifold. We prove that a precise bound on the complex Monge-Amp\`ere…
We prove exponential estimates for plurisubharmonic functions with respect to Monge-Ampere measures with Holder continuous potential. As an application, we obtain several stochastic properties for the equilibrium measures associated to…
We prove several results showing that plurisubharmonic functions with various bounds on their Monge-Ampere masses on a bounded hyperconvex domain always admit global plurisubharmonic subextension with logarithmic growth at infinity.
A class of subharmonic functions are proved to have the growth estimates $u(x)= o(x_n^{1-\frac{\alpha}{p}}|x|^{\frac{\gamma}{p}+\frac{n-1}{q}-n+\frac{\alpha}{p}})$ at infinity in the upper half space of ${\bf R}^{n}$, which generalizes the…
We study classes of convex functions on balanced polyhedral spaces and establish various structural properties, including a compactness theorem for polyhedrally plurisubharmonic functions. Using tropical intersection theory, we construct…
A C^2 function on C^n is called (n-1)-plurisubharmonic in the sense of Harvey-Lawson if the sum of any n-1 eigenvalues of its complex Hessian is nonnegative. We show that the associated Monge-Ampere equation can be solved on any compact…
We study the complex Monge-Amp\`ere operator in bounded hyperconvex domains of $\C^n$. We introduce a scale of classes of weakly singular plurisubharmonic functions : these are functions of finite weighted Monge-Amp\`ere energy. They…
Let $X$ be an algebraic subvariety of $\mathbb C^n$ and $\bar X$ be its closure in $\mathbb P^n.$ In their paper \cite{CGZ} Coman-Guedj-Zeriahi proved that any plurisubharmonic function with logarithmic growth on $X$ extends to a…
Our aim in this paper is to prove that if plurisubharmonic functions $u_1,. . . , u_n$, $v_1,. . ., v_n$ in the domain of definition of the complex Monge-Amp\`ere operator on a domain set $D\subset \mathbb{C}^n$ ($n\geq 1$) are such that…