4 citations · 7 across the 8 of their papers we have counts for
11 papers
Weak differentiability of metric space valued Sobolev maps
Paul Creutz, Nikita Evseev
We show that Sobolev maps with values in a dual Banach space can be characterized in terms of weak derivatives in a weak* sense. Since every metric space embeds isometrically into…
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…
An approach to metric space valued Sobolev maps via weak* derivatives
Paul Creutz, Nikita Evseev
We give a characterization of metric space valued Sobolev maps in terms of weak* derivatives. This corrects a previous result by Hajłasz and Tyson.
Triangulating metric surfaces
Paul Creutz, Matthew Romney
We prove that any length metric space homeomorphic to a surface may be decomposed into non-overlapping convex triangles of arbitrarily small diameter. This generalizes a previous r…
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…
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…
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…
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…
Majorization by Hemispheres & Quadratic Isoperimetric Constants
Paul Creutz
Let be a Banach space or more generally a complete metric space admitting a conical geodesic bicombing. We prove that every closed -Lipschitz curve may…