4 papers
Macroscopic scalar curvature bounds on surfaces
Otis Chodosh, Noa Vikman
We prove the generalized Geroch conjecture, and the corresponding hyperbolic conjecture, in dimension two.
Systolic inequalities for metric surfaces via filling minimality
Toni Ikonen, Denis Marti, Noa Vikman
We prove optimal systolic inequalities for length spaces homeomorphic to a torus of genus one or a real projective plane. In both cases, the optimal constant coincides with the con…
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…