Second order rectifiability of integral varifolds of locally bounded first variation

Details Second order rectifiability of integral varifolds of locally bounded first variation Second order rectifiability of integral varifolds of locally bounded first variation

2008-08-27

arxiv.org/abs/0808.3665v3

Mathematics

Differential Geometry

v1: 34 pages, no figures; v2: revised presentation, material of 0909.3253 and 0808.3665 reorganised, parts moved to 0909.3253v

Scientific paper

10.1007/s12220-011-9261-5

In this work it is shown that every integral varifold in an open subset of
Euclidian space of locally bounded first variation can be covered by a
countable collection of submanifolds of class C^2. Moreover, the mean curvature
of each member of the collection agrees with the mean curvature of the varifold
almost everywhere with respect to the varifold.

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