Related papers: The Levi problem on Stein spaces with singularitie…
We discuss local polynomial convexity of real analytic Levi-flat hypersurfaces in $\mathbb C^n$, $n>1$, near singular points.
We review the current status of the singularity problem in string theory for non-experts. After the problem is discussed from the point of view of supergravity, we discuss classic examples and recent examples of singularity resolution in…
In this note we discuss the Stein restriction problem on arbitrary $n$-torus, $n\geq 2$. In contrast with the usual cases of the sphere, the parabola and the cone, we provide necessary and sufficient conditions on the Lebesgue indices, by…
We investigate some cylindrically symmetric nonstationary and nonstatic solutions of Einstein field equations. We first study some physical properties of a solution which can be considered as Kasner generalization of static Levi-Civita…
In a locally finite tiling of n-dim Euclidean space by convex polytopes, each point of the space is either a vertex of at least two tiles, or no vertex at all.
We survey the problem of whether M_3 spaces are M_1 spaces.
In this paper we study the rigidity problem for sub-static systems with possibly non-empty boundary. First, we get local and global splitting theorems by assuming the existence of suitable compact minimal hypersurfaces, complementing recent…
A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects.
We present and discuss a number of known results and open problems abelian squares in words on small alphabets.
We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.
The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code…
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…
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…
Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on Riemann surfaces) are constructed. The…
The work deals with the Ericksen-Leslie System for nematic liquid crystals on the whole space. In our work we suppose the initial condition of the orientation field stays on an arc connecting two fixed orthogonal vectors on the unit sphere.…
This paper concerns the number of lattice points in a circle.
This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.
In this work we present a general introduction to the Signorini problem (or thin obstacle problem). It is a self-contained survey that aims to cover the main currently known results regarding the thin obstacle problem. We present the theory…
We prove that the multidimensional dimensional initial value problem for the Navier-Stokes equations is globally well-posed in the so-called Moment and Grand Lebesgue Spaces (GLS), and give some a priory estimations for solution in this…
This is a list of several open problems dealing mainly with univariate polynomials.