6 papers
CAT(0) spaces without linear filling at the asymptotic rank
Stephan Stadler
For every integer , we construct a -dimensional, locally compact, geodesically complete CAT(0) space of asymptotic rank which does not satisfy a linear isoperim…
Isoperimetric inequalities in Hadamard spaces of asymptotic rank two
Urs Lang, Stephan Stadler, David Urech
Gromov's isoperimetric gap conjecture for Hadamard spaces states that cycles in dimensions greater than or equal to the asymptotic rank admit linear isoperimetric filling inequalit…
Minimal tetrahedra and an isoperimetric gap theorem in non-positive curvature
Cornelia Druţu, Urs Lang, Panos Papasoglu +1
We investigate isoperimetric inequalities for Lipschitz 2-spheres in CAT(0) spaces, proving bounds on the volume of efficient null-homotopies. In one dimension lower, it is known t…
Rigidity of ideal symmetric sets
Stephan Stadler
We characterize higher rank model geometries -- Riemannian symmetric spaces, Euclidean buildings and products -- among Hadamard spaces by using antipodal sets at infinity.
Isoperimetric inequalities vs. upper curvature bounds
Stephan Stadler, Stefan Wenger
The Dehn function of a metric space measures the area necessary in order to fill a closed curve of controlled length by a disc. As a main result, we prove that a length space has c…
CAT(0) spaces of higher rank II
Stephan Stadler
This belongs to a series of papers motivated by Ballmann's Higher Rank Rigidity Conjecture. We prove the following. Let be a CAT(0) space with a geometric group action. Suppose…