4 papers
Ultralimits of Sobolev maps and stability of Dehn functions
Toni Ikonen, Stefan Wenger
We show that the ultralimit of a bounded sequence of Lipschitz maps into pointed metric spaces extends naturally to -bounded sequences of Sobolev maps and that this ultralimit f…
Monotone Sobolev extensions in metric surfaces and applications to uniformization
Damaris Meier, Noa Vikman, Stefan Wenger
We prove a monotone Sobolev extension theorem for maps to Jordan domains with rectifiable boundary in metric surfaces of locally finite Hausdorff 2-measure. This is then used to pr…
Energy minimizing harmonic 2-spheres in metric spaces
Damaris Meier, Noa Vikman, Stefan Wenger
In their seminal 1981 article, Sacks-Uhlenbeck famously proved the existence of non-trivial harmonic 2-spheres in every closed Riemannian manifold with non-zero second homotopy gro…
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…