Calculus of Variations and Geometric Measure Theory

G. De Philippis - C. Gasparetto - F. Schulze

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

created by dephilipp on 05 Jun 2023
modified by gasparetto on 25 Jan 2024


Published Paper

Inserted: 5 jun 2023
Last Updated: 25 jan 2024

Journal: International Mathematics Research Notices
Year: 2023

ArXiv: 2306.02490v3 PDF


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.