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Height estimate and
slicing formulas in the Heisenberg group
Roberto Monti and Davide Vittone |
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Vol. 8 (2015), No. 6, 1421–1454
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DOI: 10.2140/apde.2015.8.1421
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Abstract |
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We prove a height estimate (distance from the tangent hyperplane) for -minimizers of the perimeter in the sub-Riemannian Heisenberg group. The estimate is in terms of a power of the excess (-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
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Mathematical Subject Classification 2010
Primary: 49Q05, 53C17
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Milestones
Received: 7 October 2014
Accepted: 11 May 2015
Published: 5 September 2015
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Authors |
| Roberto Monti | |
| Dipartimento di Matematica Universitá di Padova via Trieste 63 I-35121 Padova Italy |
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| 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 |
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