A general regularity theory for weak mean curvature flow

Details A general regularity theory for weak mean curvature flow A general regularity theory for weak mean curvature flow

2011-11-03

arxiv.org/abs/1111.0824v2

Mathematics

Analysis of PDEs

60 pages

Scientific paper

We give a new proof of Brakke's partial regularity theorem up to C^{1,\varsigma} 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.

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