A Short Proof of Allard's and Brakke's Regularity Theorems

Guido De Philippis, Carlo Gasparetto, Felix Schulze

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)7594-7613
Number of pages20
JournalInternational Mathematics Research Notices
Issue number9
StatePublished - May 1 2024

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'A Short Proof of Allard's and Brakke's Regularity Theorems'. Together they form a unique fingerprint.

Cite this