Metric theory has undergone a dramatic phase transition in the last decades when its focus
moved from the foundations of real analysis to Riemannian geometry and algebraic …

Abstract The Gromov–Hausdorff distance between metric spaces appears to be a useful tool
for modeling some object matching procedures. Since its conception it has been mainly …

It is well known that Lie groups and homogeneous spaces provide a rich source of
interesting examples for a variety of geometric aspects. Likewise it is often the case that …

The purpose of this paper is to present an optimal sphere theorem for metric spaces
analogous to the celebrated Rauch-Berger-Klingenberg Sphere Theorem and the Diameter …

We prove that, if a finite metric space is of strictly negative type, then its transfinite diameter is
uniquely realized by the infinite extender (load vector). Finite metric spaces that have this …

A basic question one asks in Riemannian geometry is: how are geometric properties of a
manifold reflected in its topology? An analogous question in transformation groups is: what …

We prove that a locally compact space with an upper curvature bound is a topological
manifold if and only if all of its spaces of directions are homotopy equivalent and not …

The symmetry rank of a Riemannian manifold is the rank of the isometry group. We
determine precisely which closed simply connected 5-manifolds admit positively curved …

We obtain a structure theorem for closed, cohomogeneity one Alexandrov spaces and we
classify closed, cohomogeneity one Alexandrov spaces in dimensions 3 and 4. As a …

Stability of Convex Spheres | International Mathematics Research Notices | Oxford
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