A Notable Family of Entire Intrinsic Minimal Graphs in the Heisenberg Group which are not Perimeter Minimizing

By D. Danielli, Nicola Garofalo, D. Nhieu. 2006

57 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1c87c7dca5f6513642cdf294922e870374405d81

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In Applied Mathematics

In Astronomy and Astrophysics

In Computational Theory and Mathematics

Citations in the corpus

Regularity of non-characteristic minimal graphs in the Heisenberg group $H^1$ (2008, methodology): “For other aspects of minimal surfaces in the Heisenberg group, including classification and Bernstein-type results, see [8, 27, 2, 22, 21, 37, 36, 35].”
Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity (2008, methodology): “where they obtain regularity properties of an Hregular surfacefrom regularity propertiesof its horizontal unit normal. Interesting examples ofminimal surfaceswhich arenot area-minimizingareobtainedin [11]. Seealso[13]. Smoothness of lipschitzminimal intrinsic graphsin HeisenberggroupsHn,for n >1,”
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]).”
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].”
Sub-Riemannian calculus on hypersurfaces in Carnot groups (2006, methodology): “For an extensive bibliography we refer the reader to the recent monographs [10,27] (see also the forthcoming book [47]), and to the papers [ 26 ,28].”
TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS (2007, background): “Calculus and Analysis in stratified groups have been developed by several authors with a vast literature, here we mention a list of references for a rough overview that is certainly far from being complete, [1], [3], [4], [7], [8], [9], [11], [12], [13], [14], [ 15 ], [20], [21], [22], [24], [28], [”