Calculus of Variations and Geometric Measure Theory
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R. Monti - D. Vittone

Height estimate and slicing formulas in the Heisenberg group

created by vittone on 07 Oct 2014
modified by monti on 04 Nov 2016

[BibTeX]

Published Paper

Inserted: 7 oct 2014
Last Updated: 4 nov 2016

Journal: Analysis and PDE
Volume: 8
Number: 6
Pages: 1321-1454
Year: 2015
Doi: DOI: 10.2140/apde.2015.8.1421

Abstract:

We prove a height-estimate (distance from the tangent hyperplane) for $\Lambda$-minima of the perimeter in the sub-Riemannian Heisenberg group. The estimate is in terms of a power of the excess ($L^2$-mean oscillation of the normal) and its proof is based on a new coarea formula for rectifiable sets in the Heisenberg group.

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