Related papers: Open problems in pluripotential theory
We state an open problem in the theory of diversities: what is the worst case minimal distortion embedding of a diversity on $n$ points in $\ell_1$. This problem is the diversity analogue of a famous problem in metric geometry: what is the…
We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several…
We study the double obstacle problem for p-harmonic functions on arbitrary bounded nonopen sets E in quite general metric spaces. The Dirichlet and single obstacle problems are included as special cases. We obtain Adams' criterion for the…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
Classifications of irreducible components of the set of polynomial differential equations with a fixed degree and with at least one center singularity lead to some other new problems on Picard-Lefschetz theory and Brieskorn modules of…
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…
In this note, we propose some open problems and questions about bounded convex domains in $\mathbb C^N$, specifically about visibility and iteration theory.
The paper surveys open problems and questions related to geodesics defined by Riemannian, Finsler, semi Riemannian and magnetic structures on manifolds.
A problem list in singularity theory. Most of these problems are related with the algorithmic enumeration of possible topological types of non-discriminant Morsifications of real function singularities, and/or with the Picard--Lefschetz…
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…
We give an overview of the derivation of multipolar equations of motion of extended test bodies for a wide set of gravitational theories beyond the standard general relativistic framework. The classes of theories covered range from simple…
The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea…
We list and discuss the background of some open problems, regarding the principle of local reflexivity for maximal Banach ideals.
We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those…
The goal of this survey is to give a list of resent results about topology of manifolds admitting different metrics with the same geodesics. We emphasize the role of the theory of integrable systems in obtaining these results.
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…
We suggest a homotopical description of the Poisson bracket invariants for tuples of closed sets in symplectic manifolds. It implies that these invariants depend only on the union of the sets along with topological data.