Related papers: Perimeters, uniform enlargement and high dimension…
Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…
We consider an isoperimetric problem involving the smallest positive and largest negative curl eigenvalues on abstract ambient manifolds, with a focus on the standard model spaces. We in particular show that the corresponding eigenvalues on…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
In this article, we investigate the centered isoperimetric inequality on Cartan-Hadamard manifolds endowed with a warped product structure, namely, among all bounded measurable sets of finite perimeter and prescribed volume, the geodesic…
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…
We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon. The statement is true in spherical geometry and hyperbolic…
Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…
In this work, we investigate the continuity of the free boundary in a class of elliptic problems, with Neuman boundary condition. The main idea is a change of variable that allows us to reduce the problem to the one studied in [14].
A recent suggestion has been made that the hydrogen bound state spectrum should not depend on the number of spatial dimensions. It is pointed out here that the uncertainty principle implies that such differences must exist and that a…
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for…
The reverse isoperimetric problem asks for existence and properties of bounded convex sets in a Riemannian manifold which maximise the perimeter under all those sets of fixed volume which roll freely in a ball of some given radius. If the…
This paper is devoted to the Moser-Trudinger inequality on smooth riemanniansurfaces. We establish that the constants involved can be chosen to depend on only 3parameters, which are the systole, isoperimetric constant and curvature of the…