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math.MG2026
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…
math.MG2026
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…