Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation
Camillo De Lellis, Emanuele Spadaro, Luca Spolaor · Zurich Open Repository and Archive (University of Zurich) · 2018
We construct Lipschitz Q-valued functions which carefully approximate integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of 2-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of 3-dimensional area minimizing cones.