Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation
Camillo De Lellis, Emanuele Spadaro, and Luca Spolaor
Contact the author: Please use for correspondence this email.
Submission date: 15. Sep. 2015
published in: Transactions of the American Mathematical Society (2017), pp not yet known
DOI number (of the published article): 10.1090/tran/6995
Download full preprint: PDF (453 kB)
We construct Lipschitz Q-valued functions which approximate carefully 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.