arXiv subjects

Stefan Wenger

Publications and source records attributed to Stefan Wenger.

39 records · Page 3Linked to original sources

arXiv2006

Filling invariants at infinity and the Euclidean rank of Hadamard spaces

In this paper we study a homological version of the higher-dimensional divergence invariants defined by Brady and Farb. We show that they are quasi-isometry invariants in the class of proper cocompact Hadamard spaces in the sense of Alexandrov and that they can moreover be used to detect the Euclidean rank of such spaces. We thereby extend results of Brady-Farb, Leuzinger, and Hindawi from the setting of symmetric spaces of non-compact type to that of singular Hadamard spaces. Finally, we exhibit the optimal power for the growth of the divergence above the rank for symmetric spaces of non-compact type and for Hadamard spaces with strictly negative upper curvature bound.

math.DG↗

arXiv2005

Flat convergence for integral currents in metric spaces

It is well known that in compact local Lipschitz neighborhood retracts in Euclidean space flat convergence for integer rectifiable currents amounts just to weak convergence. In the present paper we extend this result to integral currents in complete metric spaces admitting a local cone type inequality. These include in particular all Banach spaces as well as complete CAT(k)-spaces (metric spaces of curvature bounded above by k in the sense of Alexandrov). The main result can be used to prove the existence of minimal elements in a fixed Lipschitz homology class in compact metric spaces admitting local cone type inequalities or to conclude that integral currents which are weak limits of sequences of absolutely area minimizing integral currents are again absolutely area minimizing.

math.DG↗

arXiv2003

Isoperimetric inequalities of euclidean type in metric spaces

In this paper we prove an isoperimetric inequality of euclidean type for complete metric spaces admitting a cone-type inequality. These include all Banach spaces and all complete, simply-connected metric spaces of non-positive curvature in the sense of Alexandrov or, more generally, of Busemann. The main theorem generalizes results of Gromov and Ambrosio-Kirchheim.

math.FA↗