46 citations · 317 across the 42 of their papers we have counts for
6 papers · 1 filter
CAT(0) 4-manifolds are Euclidean
Alexander Lytchak, Koichi Nagano, Stephan Stadler
We prove that a topological 4-manifold of globally non-positive curvature is homeomorphic to Euclidean space.
Weak topology on CAT(0) spaces
Alexander Lytchak, Anton Petrunin
We analyze weak convergence on CAT(0) spaces and the existence and properties of corresponding weak topologies.
Curvature bounds of subsets in dimension two
Alexander Lytchak, Stephan Stadler
We show that closed subsets with vanishing first homology in two-dimensional spaces inherit the upper curvature bound from their ambient spaces and discuss topological applications…
Cyclic projections in Hadamard spaces
Alexander Lytchak, Anton Petrunin
We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Mi…
About every convex set in any generic Riemannian manifold
Alexander Lytchak, Anton Petrunin
We give a necessary condition on a geodesic in a Riemannian manifold that can run in some convex hypersurface. As a corollary we obtain peculiar properties that hold true for every…
Remarks on manifolds with two sided curvature bounds
Vitali Kapovitch, Alexander Lytchak
We discuss folklore statements about distance functions in manifolds with two sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.