#### 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
##### Milestones
Received: 7 October 2014
Accepted: 11 May 2015
Published: 5 September 2015
##### Authors
 Roberto Monti Dipartimento di Matematica Universitá di Padova via Trieste 63 I-35121 Padova Italy Davide Vittone Dipartimento di Matematica Universitá di Padova via Trieste 63 I-35121 Padova Italy Institut für Mathematik Universität Zürich Winterthurerstrasse 190 CH-8057 Zürich Switzerland