4 citations · 7 across the 8 of their papers we have counts for
5 papers · 1 filter
Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces
Giuliano Basso, Paul Creutz, Elefterios Soultanis
In this paper we consider metric fillings of convex bodies. We show that convex bodies are the unique minimal fillings of their boundary metrics among all i…
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…
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…
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…
Plateau's problem for singular curves
Paul Creutz
We give a solution of Plateau's problem for singular curves possibly having self-intersections. The proof is based on the solution of Plateau's problem for Jordan curves in very ge…