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math.MG2019
Maximal metric surfaces and the Sobolev-to-Lipschitz property
Paul Creutz, Elefterios Soultanis
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated not…
math.MG2019
Space of minimal discs and its compactification
Paul Creutz
We investigate the class of geodesic metric discs satisfying a uniform quadratic isoperimetric inequality and uniform bounds on the length of the boundary circle. We show that the…