11 citations · 17 across the 8 of their papers we have counts for
15 papers
Lower curvature bounds on metric surfaces via the Bishop--Gromov inequality
Alexander Lytchak, Stephan Stadler
We characterize lower curvature bounds on metric surfaces by the Bishop--Gromov inequality for metric balls.
Existence of least-area discs
Alexander Lytchak, Stephan Stadler
We prove that every closed Lipschitz curve in Euclidean space extends to a Lipschitz disc of least area, with Lipschitz constant controlled by that of the boundary curve. Our proof…
Rank Rigidity for CAT(0) spaces without 3-flats
Stephan Stadler
If a group acts geometrically on a CAT(0) space without 3-flats, then either contains a -periodic geodesic which does not bound a flat half-plane, or else is a r…
CAT(0) spaces of higher rank I
Stephan Stadler
A CAT(0) space has rank at least if every geodesic lies in an -flat. Ballmann's Higher Rank Rigidity Conjecture predicts that a CAT(0) space of rank at least with a geom…
Six proofs of the Fáry--Milnor theorem
Anton Petrunin, Stephan Stadler
We sketch several proofs of Fáry--Milnor theorem.
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.
Metric minimizing surfaces revisited
Anton Petrunin, Stephan Stadler
A surface which does not admit a length nonincreasing deformation is called metric minimizing. We show that metric minimizing surfaces in CAT(0) spaces are locally CAT(0) with resp…
Monotonicity of saddle maps
Anton Petrunin, Stephan Stadler
We prove an analog of the Schoen-Yau univalentness theorem for saddle maps between discs.
Affine functions on Alexandrov spaces
Christian Lange, Stephan Stadler
We show that every finite-dimensional Alexandrov space X with curvature bounded from below embeds canonically into a product of an Alexandrov space with the same curvature bound an…
An obstruction to the smoothability of singular nonpositively curved metrics on 4-manifolds by patterns of incompressible tori
Stephan Stadler
We give new examples of closed smooth 4-manifolds which support singular metrics of nonpositive curvature, but no smooth ones, thereby answering affirmatively a question of Gromov.…