Height estimate and slicing formulas in the Heisenberg group

Monti, Roberto; Vittone, Davide

doi:10.2140/apde.2015.8.1421

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

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 $Λ$ -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

Vol. 8, No. 6, 2015