Graphs that are not complete pluripolar

Pluripolar graphs are holomorphic

We prove that the graph of a continuous function $f$, defined on a domain of ${\mathbb C}^n$, is pluripolar if and only if $f$ is holomorphic.

Graphs with multiple sheeted pluripolar hulls

In this paper we study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.

The pluripolar hull of the graph of a holomorphic function with polar singularities

We study the pluripolar hull of the graph of a holomorphic function f, defined on a domain D in the complex plane outside a polar set A of D. This leads to a theorem that describes under what conditions f is nowhere extendable over A, while the graph of f over D \ A is NOT complete pluripolar.

完全多重极集与多重次调和函数的可去奇点

Complete pluripolar sets and removable singularities of plurisubharmonic functions

本研究受已有成果启发，证明了多重次调和函数穿过紧完全多重极集的Hartogs型延拓定理，补充了Shiffman的经典定理。

The Pluripolar Hull of a Graph and Fine Analytic Continuation

We show that if the graph of a bounded analytic function in the unit disk $\mathbb D$ is not complete pluripolar in $\mathbb C^2$ then the projection of the closure of its pluripolar hull contains a fine neighborhood of a point $p \in \partial \mathbb D$. On the other hand we show that if an analytic function $f$ in $\mathbb D$ extends to a function $\mathcal{F}$ which is defined on a fine neighborhood of a point $p \in \partial \mathbb D$ and is finely analytic at $p$ then the pluripolar hull of the graph of $f$ contains the graph of $\mathcal{F}$ over a smaller fine neighborhood of $p$. We g…

Proper discs in Stein manifolds avoiding complete pluripolar sets

We prove the following theorem: Let X be a Stein manifold of dimension at least 2 and Y a closed complete pluripolar subset of X. Given a point p in the complement of Y there is a proper holomorphic map f from the unit disc to X such that f(0)=p and the image of f avoids Y.