Related papers: Barycenters in uniformly convex geodesic spaces

We provide new stable linearizability constructions for regular actions of finite groups on homogeneous spaces and low-dimensional quadrics.

We prove the existence of embedded closed constant curvature curves on convex surfaces.

We consider the optimal containment of polygonal regions within convex containers with the special property of 'orientedness' - an oriented region enables us to choose a preferred direction on the plane (this direction is not necessarily an…

Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.

We discuss self-crossing patterns of closed geodesics on a convex surface.

We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite…

We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.

The usual notion of set-convexity, valid in the classical Euclidean context, metamorphoses into several distinct convexity types in the more general Riemannian setting. By studying this phenomenon in reverse, we characterize complete…

We show that an 'almost strong Lefschetz' property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a Cohen-Macaulay complex, the $h$-vector is unimodal, peaks in…

Consider a compact surface of genus $\geq 2$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $2\pi$. Following the technique in the work of Burns, Climenhaga, Fisher, and Thompson,…

The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.

A unified version of Machado-Bishop theorem in weighted spaces is given. A number of applications illustrate its importance.

We prove a logarithm law-type result for the spiraling of geodesics around certain types of compact subsets (e.g. quotients of periodic Morse flats) in quotients of rank one CAT(0) spaces.

In this paper we investigate some generic properties of a billiard system on a convex table. We show that generically, every hyperbolic periodic point admits some homoclinic orbit.

The inviscid barotropic quasi-geostrophic equation with a free surface is considered. The free surface mandates a non-standard boundary condition. The global existence existence and uniqueness of a weak solution is established, thanks to…

In this paper we prove that geodesic mappings of (pseudo-) Riemannian manifolds preserve the class of differentiability \hbox{$(C^r, r\geq1)$}. Also, if the Einstein space $V_n$ admits a non trivial geodesic mapping onto a \hbox{(pseudo-)}…

Let $K$ be a convex body in $\mathbb{R}^n$ (i.e., a compact convex set with nonempty interior). Given a point $p$ in the interior of $K$, a hyperplane $h$ passing through $p$ is called barycentric if $p$ is the barycenter of $K \cap h$. In…

We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.

Recently, Bo'az Klartag showed that arbitrary convex bodies have Gaussian marginals in most directions. We show that Klartag's quantitative estimates may be improved for many uniformly convex bodies. These include uniformly convex bodies…

We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological 2-spheres endowed with a flat metric away from finitely many cone singularities). We use the theorem of…