We calculate the first and second variation formulae for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that move the singular set of a C^2 surface and non-singular variations for C^2_h surfaces. These formulae enable us to construct a stability operator for non-singular C^2 surfaces and another one for C^2 (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 terms of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we give a classification of the complete stable surfaces in the roto-translation group RT.

Matteo Galli (2013). First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 47, 117-157 [10.1007/s00526-012-0513-4].

First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds

GALLI, MATTEO
2013

Abstract

We calculate the first and second variation formulae for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that move the singular set of a C^2 surface and non-singular variations for C^2_h surfaces. These formulae enable us to construct a stability operator for non-singular C^2 surfaces and another one for C^2 (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 terms of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we give a classification of the complete stable surfaces in the roto-translation group RT.
2013
Matteo Galli (2013). First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 47, 117-157 [10.1007/s00526-012-0513-4].
Matteo Galli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/384348
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