Related papers: Symmetric Monge-Kantorovich problems and polar dec…

A classical result of A.D. Alexandrov states that a connected compact smooth $n-$dimensional manifold without boundary, embedded in $\Bbb R^{n+1}$, and such that its mean curvature is constant, is a sphere. Here we study the problem of…

We show continuity of solutions $u \in W^{1,n}(B^n,\mathbb{R}^N)$ to the system \[ -{\rm div} (|\nabla u|^{n-2} \nabla u) = \Omega \cdot |\nabla u|^{n-2} \nabla u \] when $\Omega$ is an $L^n$-antisymmetric potential -- and additionally…

Let $\{\mu_k\}_{k = 1}^N$ be absolutely continuous probability measures on the real line such that every measure $\mu_k$ is supported on the segment $[l_k, r_k]$ and the density function of $\mu_k$ is nonincreasing on that segment for all…

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…

In this note, following \cite{Chitescuetal2014}, we show that the Monge-Kantorovich norm on the vector space of countably additive measures on a compact metric space has a primal representation analogous to the Hanin norm, meaning that…

The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…

We discuss $SU(2)$ Bogomolny monopoles of arbitrary charge $k$ invariant under various symmetry groups. The analysis is largely in terms of the spectral curves, the rational maps, and the Nahm equations associated with monopoles. We…

Recently, Bercovici has introduced multiplicative convolutions based on Muraki's monotone independence and shown that these convolution of probability measures correspond to the composition of some function of their Cauchy transforms. We…

In this note we explicitly construct top-dimensional components of the cyclic convolution varieties. These components correspond (via the geometric Satake equivalence) to irreducible summands $V(\lambda+\mu-N\beta) \subset V(\lambda)…

We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily vanishing on the boundary $\partial \Omega$. This reduces the study of the Neumann…

We construct a new invariant-the trunkenness-for volume-perserving vector fields on S^3 up to volume-preserving diffeomorphism. We prove that the trunkenness is independent from the helicity and that it is the limit of a knot invariant…

Let $\mathcal{M}$ be a semifinite von Neumann algebra and let $E$ be a symmetric function space on $(0,\infty)$. Denote by $E(\mathcal{M})$ the non-commutative symmetric space of measurable operators affiliated with $\mathcal{M}$ and…

We present a conjecture for the leading $1/N$ anomalous dimension of the scalar primary operator in $U(N)_k$ Chern-Simons theories coupled to a single fundamental field, to all orders in the t'Hooft coupling $\lambda=\frac{N}{k}$. Following…

We study the shifted convolution problem for the divisor function in function fields in the large degree limit, that is, the average value of $d(f) d(f+h)$ where $f$ runs over monic polynomials in $\mathbb{F}_q[T]$ of a given degree, and…

Attention is drawn to the mathematical equality of rights of symmetrical constituents derived affinor of a vector field in relation to its antisymmetric constituents. In this regard, raises the question not only of equitable accounting, but…

Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $P(\omega_j=0)=P(\omega_j=1)=1/2$ and all the choices are independent. For $0<a<1/2$, the measure $\mu_a$ is supported on $C_a$, the central…

Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate of a partition function for such a theory is indeed the…

We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these…

We show that (under mild assumptions) the generating function of log homology torsion of a knot exterior has a meromorphic continuation to the entire complex plane. As corollaries, this gives new proofs of (a) the Silver-Williams…