Affine functions on CAT (κ)-spaces

We describe affine functions on spaces with an upper curvature bound.     

Cyclic Projections in Hadamard Spaces

Journal of Optimization Theory and Applications - We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces,...     

Centers of Convex Subsets of Buildings

We prove that two-dimensional convex subsets of spherical buildings are either buildings or have a center.     

The curvature of orbit spaces

We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.     

Polar Foliations of Symmetric Spaces

We prove that a polar foliation of codimension at least three in an irreducible compact symmetric space is hyperpolar, unless the symmetric space has rank one. For reducible symmetric spaces of compact type, we derive decomposition results for polar foliations.     

Affine images of Riemannian manifolds

We describe all affine maps from a Riemannian manifold to a metric space and all possible image spaces.     

Isometric actions on spheres with an orbifold quotient

Mathematische Annalen - We classify representations of compact connected Lie groups whose induced action on the unit sphere has the orbit space isometric to a Riemannian orbifold.     

On Hölder continuous Riemannian and Finsler metrics

We discuss smoothness of geodesics in Riemannian and Finsler metrics.

     

Spaces with many affine functions

We describe all metric spaces that have sufficiently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.

     

The De Rham Decomposition Theorem For Metric Spaces

We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension. Received: May 2006 Accepted: December 2006