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.
A Short Proof of Allard’s and Brakke’s Regularity Theorems / De Philippis, Guido; Gasparetto, Carlo; Schulze, Felix. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2024:9(2023), pp. 7594-7613. [10.1093/imrn/rnad281]
A Short Proof of Allard’s and Brakke’s Regularity Theorems
De Philippis, Guido;Gasparetto, Carlo;
2023-01-01
Abstract
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.| File | Dimensione | Formato | |
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