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Second Order Rectifiability of Integral Varifolds of Locally Bounded First Variation

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Abstract

It is shown that every integral varifold in an open subset of Euclidean space whose first variation with respect to area is representable by integration can be covered by a countable collection of submanifolds of the same dimension of class 2 and that their mean curvature agrees almost everywhere with the variationally defined generalized mean curvature of the varifold.

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Authors and Affiliations

  1. Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), OT Golm, Am Mühlenberg 1, 14476, Potsdam, Germany

    Ulrich Menne

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  1. Ulrich Menne
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Correspondence to Ulrich Menne.

Additional information

Communicated by Steven G. Krantz.

The author acknowledges financial support via the DFG Forschergruppe 469. The major part of this work was accomplished while the author was at the University of Tübingen. Some parts were done at the ETH Zürich and the work was put in its final form at the AEI Golm. AEI publication number AEI-2008-065.

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Menne, U. Second Order Rectifiability of Integral Varifolds of Locally Bounded First Variation. J Geom Anal 23, 709–763 (2013). https://doi.org/10.1007/s12220-011-9261-5

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  • DOI: https://doi.org/10.1007/s12220-011-9261-5

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