Vol. 8, No. 6, 2015

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Height estimate and slicing formulas in the Heisenberg group

Roberto Monti and Davide Vittone

Vol. 8 (2015), No. 6, 1421–1454
DOI: 10.2140/apde.2015.8.1421
Abstract

We prove a height estimate (distance from the tangent hyperplane) for $\Lambda$-minimizers 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.

Keywords
Heisenberg group, regularity of $H$-minimal surfaces, height estimate, slicing formula
Mathematical Subject Classification 2010
Primary: 49Q05, 53C17