A short proof of Allard's and Brakke's regularity theorems
Analysis of PDEs
2024-01-18 v3 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2306.02490,
title = {A short proof of Allard's and Brakke's regularity theorems},
author = {Guido De Philippis and Carlo Gasparetto and Felix Schulze},
journal= {arXiv preprint arXiv:2306.02490},
year = {2024}
}
Comments
Final version. To appear in IMRN