Area-stationary surfaces in contact sub-riemannian manifolds

• Autores: Matteo Galli
• Directores de la Tesis: Manuel Ritoré (dir. tes.)
• Lectura: En la Universidad de Granada ( España ) en 2012
• Idioma: inglés
• ISBN: 9788490282489
• Tribunal Calificador de la Tesis: José Antonio Gálvez López (presid.) , Manuel César Rosales Lombardo (secret.) , Gian Paolo Leonardi (voc.) , Giovanna Citti (voc.) , Francesco Serra Cassano (voc.)
• Enlaces
  • Tesis en acceso abierto en: DIGIBUG
• Resumen

  • In this thesis we study topics related to area-stationary surfaces in contact sub- Riemannian manifolds.

    In Chapter 1 we prove an existence result for isoperimetric regions in contact sub- Riemannian manifolds such that the quotient by the group of contact isometries, the diffeomorphisms that preserve the contact structure and the sub-Riemannian metric, is compact. This is the analogous result to of Morgan's Riemannian one.

    In Chapter 2, we prove a necessary condition for C^2 stable minimal surfaces with empty singular set in a large class of pseudo-hermitian manifolds, that includes the uni-modular Lie groups. The condition we found involves the Webster scalar curvature W and the pseudo-hermitian torsion of the manifold, that are pseudo- hermitian invariants.

    This characterization is obtained by the study of a stability operator, which is constructed from the second variation formula of the sub-Riemannian area. We construct another stability operator that takes account the singular set. With these two tools, we give a classification of complete stable surfaces in the group of the rigid motions of the Euclidean plane RT.

    The main purpose of Chapter 3 is to generalize variation formulas for the sub- Riemannian area in contact sub-Riemannian manifolds of arbitrary dimensions.