• Título:  EL PROBLEMA DEL ACORTAMIENTO DE CURVAS ASOCIADO A UNA DENSIDAD
• Autor:  Viñado Lereu, Francisco
• Universidad:  Universitat de València (Estudi General)
• Departamento:  Matemàtiques
• Fecha de Lectura:  28/10/2016
• Programa de doctorado:  Programa Oficial de Doctorado en Matemáticas
• Dirección: 
  • MIQUEL MOLINA, VICENTE (DIRECTOR)
• Tribunal: 
  • Petrola de Melo Jorge, Luquesio (PRESIDENTE)
  • GIL MEDRANO, OLGA (SECRETARIO)
  • Castro López, Ildefonso (VOCAL)
• Descriptores: 
  • MATEMATICAS
  • GEOMETRIA DIFERENCIAL
  • ECUACIONES DIFERENCIALES EN DERIVADAS PARCIALES
  • GEOMETRIA DE RIEMANN
• Localización:  BIBLIOTECA DE CIENCIES EDUARD BOSCÀ - BURJASSOT
• 288717_880114.pdf
• Resumen:
  In this Thesis we study the mean curvature flow associated to the density (psi-mean curvature flow or psiMCF) of a hypersurface in a Riemannian manifold with density. In the chapter two, the main results concern with the description of the evolution under psiMCF of a closed embedded curve in the plane with a radial density, and with a statement of subconvergence to a psi-minimal closed curve in a surface under some general circumstances. In the chapter three, we define Type I singularities for the mean curvature flow associated to a density psi and describe the blow-up at singular time of these singularities. Special attention is paid to the case where the singularity come from the part of the psi-curvature due to the density. We describe a family of curves whose evolution under psiMCF (in a Riemannian surface of non-negative curvature with a density which is singular at a geodesic of the surface) produces only type I singularities and study the limits of their blow-ups.