46 citations · 317 across the 42 of their papers we have counts for
4 papers · 1 filter
Isoperimetric characterization of upper curvature bounds
Alexander Lytchak, Stefan Wenger
We prove that a proper geodesic metric space has non-positive curvature in the sense of Alexandrov if and only if it satisfies the Euclidean isoperimetric inequality for curves. Ou…
Dehn functions and Hölder extensions in asymptotic cones
Alexander Lytchak, Stefan Wenger, Robert Young
The Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are s…
The curvature of orbit spaces
Claudio Gorodski, Alexander Lytchak
We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.
Intrinsic structure of minimal discs in metric spaces
Alexander Lytchak, Stefan Wenger
We study the intrinsic structure of parametric minimal discs in metric spaces admitting a quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic…