相关论文: Pluripolarity of Graphs of Algebroid Functions

We give a simplified proof of analyticity of pluripolar multifunctions

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning set

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.

We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a…

Let A be a closed polar subset of a domain D in the complex plane C. We give a complete description of the pluripolar hull in D X C of the graph of a holomorphic function defined on D A. To achieve this, we prove for pluriharmonic measure…

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…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.

An algebraic deformation theory of coalgebra morphisms is constructed.

By the classical result of E. Bedford, a real-analytic non-generic manifold is pluripolar. We extend this result for manifolds of the Gevrey class. This also gives a generalization of the recent result of D. Coman, N. Levenberg and E.…

The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.

We prove the the multipole Lempert function is monotone under inclusion of pole sets.

We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.

Examples by Poletsky and the author and by Zwonek show the existence nowhere extendable holomorphic functions with the property that the pluripolar hull of their graphs is much larger than the graph of the respective functions and contains…

$J$-holomorphic curves are pluripolar, but they are not minus-infinity sets of pluri-subharmonic functions with logarithmic singularity.

We present the theory of multifunctions applied to graphs. Its interesting feature is that walks are recognized as iterations. We consider the graphs with arbitrary number of vertices which are determined by multifunctions. The mutually…

We classify which complete multipartite graphs are intrinsically chiral.

We prove that the image of a finely holomorphic map on a fine domain in $\mathbb{C}$ is pluripolar subset of $\mathbb{C}^{n}$. We also discuss the relationship between pluripolar hulls and finely holomorphic function.

An algebraic deformation theory of dialgebra morphisms is obtained.