Ir al contenido

Documat


Area-stationary surfaces in contact sub-riemannian manifolds

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


Fundación Dialnet

Mi Documat

Opciones de tesis

Opciones de compartir

Opciones de entorno