Curvature flows, solutions quenching in finite time and asymptotic behavior

Author(s)

Rafael Rodrigo Ottoboni

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2011-09-15

Examining board members

Marcelo da Silva Montenegro; Francisco Odair Vieira de Paiva; Pedro Jose Catuogno; Sebastian Antonio Lorca Pizarro; Eugenio Tommaso Massa

• Advisor: Marcelo da Silva Montenegro

Abstract

In this thesis we present results on mean curvature flow, Gaussian curvature flow and harmonic mean curvature flow subject to boundary conditions of Dirichlet type, Neumann or singular. Solutions to some of curvature flows with some of these boundary conditions quench in finite time or exist globally in time and converge to a straight line (AU)