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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang


IMPACT FACTOR 2018: 2.316

CiteScore 2018: 1.77

SCImago Journal Rank (SJR) 2018: 2.350
Source Normalized Impact per Paper (SNIP) 2018: 1.465

Mathematical Citation Quotient (MCQ) 2018: 1.44

Online
ISSN
1864-8266
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Volume 7, Issue 4

Issues

Graphs of bounded variation, existence and local boundedness of non-parametric minimal surfaces in Heisenberg groups

Francesco Serra Cassano / Davide Vittone
Published Online: 2013-05-04 | DOI: https://doi.org/10.1515/acv-2013-0105

Abstract

In the setting of the sub-Riemannian Heisenberg group ℍn, we introduce and study the classes of t- and intrinsic graphs of bounded variation. For both notions we prove the existence of non-parametric area-minimizing surfaces, i.e., of graphs with the least possible area among those with the same boundary. For minimal graphs we also prove a local boundedness result which is sharp at least in the case of t-graphs in ℍ1.

Keywords: Minimal surfaces; bounded variation; Heisenberg group; sub-Riemannian geometry

MSC: 49Q05; 53C17; 49Q15

About the article

Received: 2013-03-15

Accepted: 2013-04-08

Published Online: 2013-05-04

Published in Print: 2014-10-01


Funding Source: INDAM

Award identifier / Grant number: GALA

Funding Source: INDAM

Award identifier / Grant number: MIUR

Funding Source: INDAM

Award identifier / Grant number: GNAMPA

Funding Source: University of Trento, Italy

Funding Source: University of Padova, Italy

Funding Source: Fondazione CaRiPaRo

Award identifier / Grant number: Project “Nonlinear Partial Differential Equations: models, analysis, and control-theoretic problems”


Citation Information: Advances in Calculus of Variations, Volume 7, Issue 4, Pages 409–492, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2013-0105.

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