# RECTIFIABILITY PROPERTIES OF VARIFOLDS IN l3∞

• Zhao, Peibiao (Department of Applied Mathematics Nanjing University of Science and Technology) ;
• Yang, Xiaoping (Department of Applied Mathematics Nanjing University of Science and Technology)
• Published : 2007.02.28
• 92 7

#### Abstract

We prove the following theorem: Given a Varifold V in $l^{3}_{\infty}$ with the property that 0 < $lim_{r}_{\rightarrow}_{o}\;\frac{{\mu}v(C_{r}(x))}{r^{2}}\;<\;{\infty}\;for\;{\mu}v\;a.e.x\;{\in}$ SptV, then V is rectifiable.

#### Keywords

Varifolds;tangent measures;rectifiable sets;rectifiable measures

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