Related papers: Open problems in pluripotential theory

For the bi-orthogonal polynomials with the third degree polynomial potential functions, the 3 x 3 matrix Riemann-Hilbert problem is explicitly constructed. The developed approach admits an extension to the bi-orthogonal polynomials with…

New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…

We propose a list of open problems in numerical semigroups.

I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.

We prove that every locally pluripolar set on a compact complex manifold is pluripolar. This extends similar results in K\"ahler case.

We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…

In this paper we prove the basic facts for pluricomplex Green functions on manifolds. The main goal is to establish properties of complex manifolds that make them analogous to relatively compact or hyperconvex domains in Stein manifolds.…

In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.

Our aim is to solve a quite old question on the difference between expandability and compact expandability. Toward this, we further investigate the logic of countable cofinality.

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

This is a selection of open problems dealing with ``large'' (non locally compact) topological groups and concerning extreme amenability (fixed point on compacta property), oscillation stability, universal minimal flows and other aspects of…

An overview of the recent developments in plurifine potential theory.

I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic analog of the P v. NP problem.

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…

In this paper we solve the Dirichlet problems for different classes of plurisubharmonic functions on compact sets in $\mathbb C^n$ including continuous, pluriharmonic and maximal functions.

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.

We develop potential theory for $m$-subharmonic functions with respect to a Hermitian metric on a Hermitian manifold. First, we show that the complex Hessian operator is well-defined for bounded functions in this class. This allows to…

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…

This paper develops a theory of polynomial maps from commutative semigroups to arbitrary groups and proves that it has desirable formal properties when the target group is locally nilpotent. We apply this theory to solve Waring's Problem…