Calculus of Variations and Geometric Measure Theory

C. De Lellis - J. Hirsch - A. Marchese - S. Stuvard

Area minimizing currents mod $2Q$: linear regularity theory

created by stuvard on 10 Sep 2019
modified on 16 Jan 2022


Published Paper

Inserted: 10 sep 2019
Last Updated: 16 jan 2022

Journal: Comm. Pure Appl. Math.
Volume: 75
Number: 1
Pages: 83-127
Year: 2022
Doi: 10.1002/cpa.21964

ArXiv: 1909.03305 PDF
Links: CPAM


We establish a theory of $Q$-valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents $\mathrm{mod}(p)$ when $p=2Q$, and to establish a first general partial regularity theorem for every $p$ in any dimension and codimension.

Keywords: Dirichlet energy, Area minimizing currents mod(p), Multiple valued functions, Regularity of solutions of variational problems