Related papers: Open problems in pluripotential theory

In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…

This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…

we study on compact Riemannian manifolds with boundary, the problems of existence and multiplicity of solutions to a Neumann problem involving the p-Laplacian operator and critical Sobolev exponents.

We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.

This is the second in a series of papers. Here we develop here an intersection theory for manifolds equipped with an action of a finite group. As in our previous paper, our approach will be homotopy theoretic, enabling us to circumvent the…

This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…

We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…

Extending a recent theory developed on compact K\"ahler manifolds by Guedj-Lu-Zeriahi and the author, we define and study pluripotential solutions to degenerate parabolic complex Monge-Amp\`ere equations on compact Hermitian manifolds.…

We study the existence of solutions to systems of ordinary differential equations that involve the p-Laplacian for potentials with several global minima. We consider the connection problem for potentials with two minima in arbitrary…

We define a simpler notion of symmetric topological complexity more ad hoc to the motion planning problem which was the original motivation for the definition of topological complexity. This is a homotopy invariant that we call…

Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., {\it Generalized distances and their associate metrics. Impact on fixed point theory}, Creat. Math. Inform. {\bf 22} (2013), no. 1,…

The relations between integrable Poisson algebras with three generators and two-dimensional manifolds are investigated. Poisson algebraic maps are also discussed.

The work in this paper is to initiate a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its…

We present five open problems in the theory of vertex rings. They cover a variety of different areas of research where vertex rings have been, or are threatening to be, relevant. They have also been chosen because I personally find them…

The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…

This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…

We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.

These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called…

We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i.) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii.)…