A second derivative H\"{o}lder estimate for weak mean curvature flow

Abstract

We give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given \alpha-H\"{o}lder continuous vector field, then we show C^{2,\alpha} regularity almost everywhere.