A Short Proof of Allard’s and Brakke’s Regularity Theorems-Reference-Cited by-同舟云学术

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

Published:2023-11-23 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

De Philippis Guido¹,Gasparetto Carlo²,Schulze Felix³

Affiliation:

1. Courant Institute of Mathematical Sciences, New York University , 251 Mercer Street, New York, NY 10012, USA

2. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5 , 56127 Pisa, Italy

3. Department of Mathematics, Zeeman Building, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL, UK

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnad281/53712166/rnad281.pdf

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