%0 Journal Article
%T First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds
%A Matteo Galli
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s00526-012-0513-4
%X We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator for non-singular C^2 surfaces and another one for C2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we classify complete stable surfaces in the roto-traslation group RT .
%U http://arxiv.org/abs/1109.6213v2