A second derivative Hölder estimate for weak mean curvature flow

By Yoshihiro Tonegawa. 2012

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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 α-Hölder continuous vector field, then we show the regularity almost everywhere.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/90a4ff78db175005344f3e0e2576f883c171b758