The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
By Vittorio Barone Adesi, Francesco Serra Cassano, Davide Vittone. 2006
93 citations recorded by the source corpus.
In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Carathéodory (CC) structures. More precisely we will introduce a general calibration method in this setting and we will study the Bernstein problem for entire regular intrinsic minimal graphs in a meaningful and simpler class of CC spaces, i.e. the Heisenberg group $${\mathbb{H}^n}$$ . In particular we will positively answer to the Bernstein problem in the case n = 1 and we will provide counter examples when $${n\geq 5}$$ .
Subfields: Applied Mathematics, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/508493afe3abc6331647f36a5da8639c2fab44bb
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In Applied Mathematics
- Manuel Ritor'e
- Giovanna Citti
- Maria Manfredini
- Luca Capogna
- Nicola Garofalo
- D. Danielli
- D. Nhieu
- Francesco Serra Cassano
In Computational Mechanics
Citations in the corpus
- Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs (2009, background): “The latter has been in the framework of minimal surfaces in Hn (see [24],[10], [ 3 ],[11], [6] and [7]).”
- Sub-Riemannian calculus on hypersurfaces in Carnot groups (2006, methodology): “Using also the results in [DGN3], in [BSV] the authors have provided a positive answer to this conjecture.”
- Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity (2008, methodology): “solutions of the Bernstein problem for C2 surfaces has been obtained by Cheng, Hwang, Malchiodi and Yang [8], and Ritor´e and Rosales [29] for tgraphs, and by Barone Adessi, Serra Cassano and Vittone [4] and Garofalo and Pauls [23] for vertical graphs. Additional contributions concerning variational”
- Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1 (2010, background): “Properties of regular minimal surfaces have been investigated in [24], [31], [8], [7], [23], [19], [2] and [29].”