Related papers: Some recent applications of the barycenter method …

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic…

The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…

Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…

In this work, we review the concept of center of a geometric object as an equivariant map, unifying and generalizing different approaches followed by authors such as C. Kimberling or A. Edmonds. We provide examples to illustrate that this…

The analysis of the affect of angular velocity on the geometry of the basins of convergence (BoC) linked to the equilibrium points in the restricted three-body problem is illustrated when the primaries are source of radiation. The bivariate…

We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections, we retrieve familiar weighted least-squares gradients, but…

In this article we apply the machinery developed in Guo-Iyer[1] together with a new compactness estimate and an object called the degree in order to prove validity of steady Prandtl layer expansions with external forcing.

The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat…

Computational methods are an important tool for solving the Yang-Baxter equations(in small dimensions), for classifying (unifying) structures, and for solving related problems. This paper is an account of some of the latest developments on…

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

We establish global existence of mild solutions to the BGK model proposed by Bouchut [J. Stat. Phys., 95, (1999), 113--170] under the minimal assumption of finite kinetic entropy initial data. Moreover we rigorously derive a kinetic entropy…

The first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties. Our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all…

We study in details the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko for a large class of densities on $\mathbb{R}^d$. We then use the work of Bickel and Breiman to prove a central limit theorem in…

G.A. Galperin introduced the axiomatic mass center system for finite point sets in spherical and hyperbolic spaces, proving the uniqueness of the mass center system. In this paper, we revisit this system and provide a significantly simpler…

We present a new proof of the bi-Lipschitz model theorem, which occupies the main part of the Ending Lamination Conjecture proved by Minsky and Brock-Canary-Minsky. Our proof is done by using techniques of standard hyperbolic geometry as…

In the recent papers~[18],~[5], respectively, the existence of motions where the perihelions afford periodic oscillations about certain equilibria and the onset of a topological horseshoe have been proved. Such results have been obtained…

Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…

A surgery classification theory is introduced for manifolds of bounded geometry up to quasi-isometry. The Borel conjecture for this theory is proven for flat Euclidean space.

We exhibit differential geometric structures that arise in numerical methods, based on the construction of Cauchy sequences, that are currently used to prove explicitly the existence of weak solutions to functional equations. We describe…

Motivated by recent findings on the derivation of parametric non-involutive solutions of the Yang-Baxter equation we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new…