A Sobolev Poincaré type inequality for integral varifolds

  • Ulrich MenneEmail author
Open Access


In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.

Mathematics Subject Classification (2000)

Primary 49Q15 Secondary 29B05 



The author acknowledges financial support via the Forschergruppe no. 469 of the Deutsche Forschungsgemeinschaft. The research was carried out while the author was a PhD student at the University of Tübingen and put in its final form while the author was at the AEI Golm and the ETH Zürich. AEI publication number: AEI-2008-064.

The author offers his thanks to Professor Reiner Schätzle for guiding him during the preparation of the underlying dissertation as well as interesting discussions about various mathematical topics. The author would also like to thank Professor Tom Ilmanen for his invitation to the ETH in Zürich in 2006, and for several interesting discussions concerning considerable parts of this work.

Open Access

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute)OT GolmPotsdamGermany

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