Related papers: A new approach to weak convergence of random cones…

First, we show that a warped product of a line and a fiber manifold is weakly conformally flat and quasi Einstein if and only if the fiber is Einstein. Next, we characterize and classify contact (in particular, $K$-contact) Riemannian…

In this paper the weak topology on a normed space is studied from the viewpoint of infinite-dimensional topology. Besides the weak topology on a normed space $X$ (coinciding with the topology of uniform convergence on finite subsets of the…

We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also…

In this paper, we argue that, in 2-d, the weak localisation of bosons, which occurs on the insulating side of the superconductor-insulator transition, is characterised by $\rho \sim ln(1/T)$, as compared to $\sigma \sim lnT$ for fermions.…

We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special…

In this brief article we characterize the relatively compact subsets of $\mathcal{A}^p$ for the topology $\sigma(\mathcal{A}^p,\mathcal{R}^q)$ (see below), by the weak compact subsets of $L^p$ . The spaces $\mathcal{R}^q$ endowed with the…

We propose a method for recovering the two-dimensional gravitational potential of galaxy clusters which combines data from weak and strong gravitational lensing. A first estimate of the potential from weak lensing is improved at the…

This note demonstrates that we can stably recover all symmetric Toeplitz matrices $\pmb{X}_0\in\mathbb{R}^{n\times n}$ of rank at most $r$ from a number of rank-one subgaussian measurements on the order of $r\log^{2} n$ with an…

We investigate weak approximation away from a finite set of places for a class of biquadratic fourfolds inside $\mathbb{P}^3 \times \mathbb{P}^2$, some of which appear in the recent work of Hassett--Pirutka--Tschinkel.

This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that the local growth of quadrangulation is governed by…

We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to…

The challenge in weak gravitational lensing caused by galaxies and clusters is to infer the projected mass density distribution from gravitational lensing measurements, known as the inversion problem. We introduce a novel theoretical…

We establish a connection between properties of partially symmetric tensors (i.e. tensors associated to linear systems of quadric hypersurfaces) and the geometry of some related loci, generalization of the Weddle loci introduced in…

Let $(X_n)$ be a sequence of random variables with values in a standard Borel space $S$. We investigate the condition \begin{gather}\label{x56w1q} E\bigl\{f(X_{n+1})\mid X_1,\ldots,X_n\bigr\}\,\quad\text{converges in probability,}\tag{*}…

We consider a family of random line tessellations of the Euclidean plane introduced in a much more formal context by Hug and Schneider [Geom. Funct. Anal. 17, 156 (2007)] and described by a parameter \alpha\geq 1. For \alpha=1 the zero-cell…

Motivated by the inverse moment problem for convex polytopes, we study the pushforward to a line of the Lebesgue measure restricted to a convex $d$-polytope. Such pushforwards are spline densities of degree $d-1$, and their moments lead…

We show that $c_0$, and in fact $C(K)$ for any scattered compact Hausdorff space $K$, have the property that finite convex combinations of slices of the unit ball are relatively weakly open.

This work investigates dense packings of congruent hard infinitesimally--thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle $\theta \in \left ( \pi, 2\pi \right ]$.…

Theory of weak localization is developed for two-dimensional holes in the presence of in-plane magnetic field. The Zeeman splitting even in the hole momentum results in the spin-dependent phase changing the quantum interference. The…

We obtain an infinite-dimensional cone of singular twisted Hilbert spaces $Z(\varphi)$ which are isomorphic to their duals but not to their conjugate duals. We do that by showing that the subset of all bi-Lipschitz maps from $[0, \infty)$…