Title: A short proof of Allard’s and Brakke’s regularity theorems
Authors: Guido De Philippis, Carlo Gasparetto, Felix Schulze
Categories: math.AP math.DG
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We give new short proofs of Allard’s regularity theorem for varifolds with
bounded first variation and Brakke’s regularity theorem for integral Brakke
flows with bounded forcing. They are based on a decay of flatness, following
from weighted versions of the respective monotonicity formulas, together with a
characterization of non-homogeneous blow-ups using the viscosity approach
introduced by Savin.
\\ ( https://arxiv.org/abs/2306.02490 , 21kb)