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.

中文翻译：

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有界平均曲率的波纹的二阶可校正性

我们证明，在密度和统一的平均曲率上具有统一下界的m维可校正变量的支持几乎可以通过m的可数并集覆盖\（{\ mathscr {H}} ^ {m} \）类\（{\ mathcal {C}} ^ {2} \）的维子流形。子流形的\（{\数学{C}} ^ {2} \） -规则性是最佳的。