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A short proof of Allard's and Brakke's regularity theorems

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arxiv 2306.02490 v3 pith:2H4XCQID submitted 2023-06-04 math.AP math.DG

Guido De Philippis , Carlo Gasparetto , Felix Schulze This is my paper
classification math.APmath.DG
keywords brakkeregularityallardboundedshorttheoremapproachblow-ups
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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.

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