Stephan Stadler

activity

20132026

most citedMetric minimizing surfaces revisited

11 citations · 17 across the 8 of their papers we have counts for

collaborators

15 papers

math.MG2026

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.

math.DG2026

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…

math.MG2022

Rank Rigidity for CAT(0) spaces without 3-flats

Stephan Stadler

If a group $Γ$ acts geometrically on a CAT(0) space $X$ without 3-flats, then either $X$ contains a $Γ$ -periodic geodesic which does not bound a flat half-plane, or else $X$ is a r…

math.MG2022

CAT(0) spaces of higher rank I

Stephan Stadler

A CAT(0) space has rank at least $n$ if every geodesic lies in an $n$ -flat. Ballmann's Higher Rank Rigidity Conjecture predicts that a CAT(0) space of rank at least $2$ with a geom…

math.HO2022

Six proofs of the Fáry--Milnor theorem

Anton Petrunin, Stephan Stadler

We sketch several proofs of Fáry--Milnor theorem.

math.DG2021★ 1 cited

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.