Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation

De Lellis, Camillo; Spadaro, Emanuele; Spolaor, Luca (2018). Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation. Transactions of the American Mathematical Society, 370(3):1783-1801.

Abstract

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.

Abstract

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.

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