open access

https://hdl.handle.net/2115/58534

A general regularity theory for weak mean curvature flow

英語

2014-05-01

Springer

Calculus of Variations and Partial Differential Equations

50(1-2)

1-68

We give a new proof of Brakke's partial regularity theorem up to for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The new proof extends to a general flow whose velocity is the sum of the mean curvature and any given background flow field in a dimensionally sharp integrability class. It is a natural parabolic generalization of Allard's regularity theorem in the sense that the special time-independent case reduces to Allard's theorem.

学術雑誌論文

Accepted Manuscript

The final publication is available at link.springer.com

0944-2669

1432-0835