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In geometric measure theory, a field of mathematics, the Almgren regularity theorem, proved by Almgren (1983, 2000), states that the singular set of a mass-minimizing surface has codimension at least 2. Almgren's proof of this was 955 pages long. Within the proof many new ideas are introduced, such as monotonicity of a frequency function and the use of a center manifold to perform a more intricate blow-up procedure.
A streamlined and more accessible proof of Almgren's regularity theorem, following the same ideas as Almgren, was given by Camillo De Lellis and Emanuele Spadaro in a series of three papers.[1]
^De Lellis, Camillo; Spadaro, Emanuele Regularity of area minimizing currents III: blow-up. Ann. of Math. (2) 183 (2016), no. 2, 577–617.
Almgren, F. J. (1983), "Q valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two", Bulletin of the American Mathematical Society, New Series, 8 (2): 327–328, doi:10.1090/S0273-0979-1983-15106-6, ISSN0002-9904, MR0684900
