The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

2006/08/03 by Vittorio Barone Adesi, Adesi, V. Barone, Fabio Cassano +3 · 3 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.math/0608092

openalex publication_date 2006/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Caratheodory (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 Hⁿ. In particular we will positively answer to the Bernstein problem in the case n=1 and we will provide counterexamples when n>=5.

Citations

• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un

Cited by

• The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups H_n
• The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group
• Plateau's Problem for intrinsic graphs in the Heisenberg Group

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