A notable family of entire intrinsic minimal graphs in the heisenberg group which are not perimeter minimizing

D. Danielli; N. Garofalo; D. M. Nhieu

doi:10.1353/ajm.2008.0013

A notable family of entire intrinsic minimal graphs in the heisenberg group which are not perimeter minimizing

D. Danielli, N. Garofalo, D. M. Nhieu

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

One of the main objectives of this paper is to unravel a new interesting phenomenon of the sub-Riemannian Bernstein problem with respect to its Euclidean ancestor, with the purpose of also indicating a possible line of attack toward its solution. We show that the global intrinsic graphs (1.2) are unstable critical points of the horizontal perimeter. As a consequence of this fact, the study of the stability acquires a central position in the problem itself.

Original language	English (US)
Pages (from-to)	317-339
Number of pages	23
Journal	American Journal of Mathematics
Volume	130
Issue number	2
DOIs	https://doi.org/10.1353/ajm.2008.0013
State	Published - Apr 2008
Externally published	Yes

Keywords

First and second variation formulas
H-minimal surfaces
Intrinsic graphs

ASJC Scopus subject areas

General Mathematics

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10.1353/ajm.2008.0013

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abstract = "One of the main objectives of this paper is to unravel a new interesting phenomenon of the sub-Riemannian Bernstein problem with respect to its Euclidean ancestor, with the purpose of also indicating a possible line of attack toward its solution. We show that the global intrinsic graphs (1.2) are unstable critical points of the horizontal perimeter. As a consequence of this fact, the study of the stability acquires a central position in the problem itself.",

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AU - Garofalo, N.

AU - Nhieu, D. M.

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AB - One of the main objectives of this paper is to unravel a new interesting phenomenon of the sub-Riemannian Bernstein problem with respect to its Euclidean ancestor, with the purpose of also indicating a possible line of attack toward its solution. We show that the global intrinsic graphs (1.2) are unstable critical points of the horizontal perimeter. As a consequence of this fact, the study of the stability acquires a central position in the problem itself.

KW - First and second variation formulas

KW - H-minimal surfaces

KW - Intrinsic graphs

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A notable family of entire intrinsic minimal graphs in the heisenberg group which are not perimeter minimizing

Abstract

Keywords

ASJC Scopus subject areas

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