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math.DG2020
The Plateau-Douglas problem for singular configurations and in general metric spaces
Paul Creutz, Martin Fitzi
Assume you are given a finite configuration of disjoint rectifiable Jordan curves in . The Plateau-Douglas problem asks whether there exists a minimizer of area a…
math.DG2020
The branch set of minimal disks in metric spaces
Paul Creutz, Matthew Romney
We study the structure of the branch set of solutions to Plateau's problem in metric spaces satisfying a quadratic isoperimetric inequality. In our first result, we give examples o…
math.DG2020
Rigidity of the Pu inequality and quadratic isoperimetric constants of normed spaces
Paul Creutz
Our main result gives an improved bound on the filling areas of closed curves in Banach spaces which are not closed geodesics. As applications we show rigidity of Pu's classical sy…