Second order rectifiability of varifolds of bounded mean curvature

Abstract

AbstractWe 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 $$ {\mathscr {H}}^{m} $$ H m almost everywhere by a countable union of m dimensional submanifolds of class $$ {\mathcal {C}}^{2} $$ C 2 . The $$ {\mathcal {C}}^{2} $$ C 2 -regularity of the submanifolds is optimal.