Year: 2023
Type: preprint
Abstract: We prove that a Sobolev map from a Riemannian manifold into a complete metric space pushes forward almost every compactly supported integral current to an Ambrosio--Kirchheim integral current in the metric target, where "almost every" is understood in a modulus sense. As an application, we prove that when the target supports an isoperimetric inequality of Euclidean type for integral currents, an isoperimetric inequality for Sobolev mappings relative to bounded, closed and additive cochains follows. Using the results above, we answer positively to an open question by Onninen and Pankka on sharp Hölder continuity for quasiregular curves. A key tool in the continuity proof is Almgren's isoperimetric inequality for integral currents.
Source: arXiv (Cornell University)
Author: Ikonen, Toni
Institution: Helsinki Institute of Physics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Academy of Finland
OpenAlex ID: W4361193789