Decay estimates for the quadratic tilt-excess of integral varifolds

Details Decay estimates for the quadratic tilt-excess of integral varifolds Decay estimates for the quadratic tilt-excess of integral varifolds

2009-09-17

arxiv.org/abs/0909.3253v3

Arch. Ration. Mech. Anal., 204:1--83, 2012

Mathematics

Differential Geometry

v3: major revision; new section "Preliminaries"; new section "A model case of partial regularity"; introduction, notation and

Scientific paper

10.1007/s00205-011-0468-1

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 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.

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