Abstract
We prove that the support of an m dimensional rectifiable varifold with a uniform lower bound on the density and bounded generalized mean curvature can be covered {mathscr {H}}^{m} almost everywhere by a countable union of m dimensional submanifolds of class {mathcal {C}}^{2} . The {mathcal {C}}^{2} -regularity of the submanifolds is optimal.
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