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- Title
A NOTABLE FAMILY OF ENTIRE INTRINSIC MINIMAL GRAPHS IN THE HEISENBERG GROUP WHICH ARE NOT PERIMETER MINIMIZING.
- Authors
Danielli, D.; Garofalo, N.; Nhieu, D. M.
- Abstract
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.
- Subjects
RIEMANNIAN geometry; GENERALIZED spaces; DIFFERENTIAL geometry; RIEMANNIAN submersions; HEISENBERG uncertainty principle
- Publication
American Journal of Mathematics, 2008, Vol 130, Issue 2, p317
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.2008.0013