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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.
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…
Improvements of upper curvature bounds
Alexander Lytchak, Stephan Stadler
We show that any space with a positive upper curvature bound has in a small neighborhood of any point a closely related metric with a negative upper curvature bound.
Ricci curvature in dimension 2
Alexander Lytchak, Stephan Stadler
We prove that in two dimensions the synthetic notions of lower bounds on sectional and on Ricci curvature coincide.
The structure of minimal surfaces in CAT(0) spaces
Stephan Stadler
We prove that a minimal disc in a CAT(0) space is a local embedding away from a finite set of "branch points". On the way we establish several basic properties of minimal surfaces:…
Conformal deformations of CAT(0) spaces
Alexander Lytchak, Stephan Stadler
We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.