Vol. 271, No. 1, 2014

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On the classification of complete area-stationary and stable surfaces in the subriemannian Sol manifold

Matteo Galli

Vol. 271 (2014), No. 1, 143–157
Abstract

We study the classification of area-stationary and stable C2 regular surfaces in the space of the rigid motions of the Minkowski plane E(1,1), equipped with its subriemannian structure. We construct examples of area-stationary surfaces that are not foliated by subriemannian geodesics. We also prove that there exist an infinite number of C2 area-stationary surfaces with a singular curve. Finally we show the stability of C2 area-stationary surfaces foliated by subriemannian geodesics.

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Keywords
subriemannian geometry, area-stationary surfaces, stable surfaces, pseudohermitian manifolds, Sol geometry
Mathematical Subject Classification 2010
Primary: 49Q05, 49Q20, 53C17
Milestones
Received: 27 May 2013
Revised: 9 August 2013
Accepted: 16 August 2013
Published: 10 September 2014
Authors
Matteo Galli
Departamento de Geometría y Topología
Universidad de Granada
18071 Granada
Spain