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Journal Article

Decay estimates for the quadratic tilt-excess of integral varifolds

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Menne,  Ulrich
Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0909.3253v1.pdf
(Preprint), 768KB

0909.3253v2.pdf
(Preprint), 747KB

0909.3253v3.pdf
(Preprint), 839KB

ARMAonline.pdf
(Any fulltext), 869KB

Arma204_1.pdf
(Any fulltext), 850KB

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Citation

Menne, U. (2012). Decay estimates for the quadratic tilt-excess of integral varifolds. Archive for Rational Mechanics and Analysis, 204(1), 1-83. doi:10.1007/s00205-011-0468-1.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-60E6-9
Abstract
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise and almost everywhere decay results for the quadratic tilt-excess are established for those varifolds. The results are optimal in terms of the dimension of the varifold and the exponent of the Lebesgue space in most cases, for example if the varifold is not two-dimensional.