We prove that, in the first Heisenberg group H, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of H. Moreover two examples are given for stressing result’s sharpness.

The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group / Nicolussi, S.; Serra Cassano, F.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 58:4(2019), pp. 1-28. [10.1007/s00526-019-1581-5]

The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group

Nicolussi S.;Serra Cassano F.
2019

Abstract

We prove that, in the first Heisenberg group H, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of H. Moreover two examples are given for stressing result’s sharpness.
4
Nicolussi, S.; Serra Cassano, F.
The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group / Nicolussi, S.; Serra Cassano, F.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 58:4(2019), pp. 1-28. [10.1007/s00526-019-1581-5]
File in questo prodotto:
File Dimensione Formato  
Nicolussi_SerraCassano_calcvar.pdf

Solo gestori archivio

Descrizione: Articolo principale
Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 685.94 kB
Formato Adobe PDF
685.94 kB Adobe PDF   Visualizza/Apri
1809.04586.pdf

accesso aperto

Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 835.1 kB
Formato Adobe PDF
835.1 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/252971
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 3
social impact