El problema del acortamiento de curvas asociado a una densidad

• Autores: Francisco Viñado Lereu
• Directores de la Tesis: Vicente F. Miquel Molina (dir. tes.)
• Lectura: En la Universitat de València ( España ) en 2016
• Idioma: español
• Número de páginas: 165
• Tribunal Calificador de la Tesis: Luquésio Petrola De melo Jorge (presid.) , Olga Gil Medrano (secret.) , Ildefonso Castro López (voc.)
• Enlaces
  • Tesis en acceso abierto en: RODERIC
• 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.