Superfícies mínimas completas e estáveis em R3

Abstract

In this work we are interested in replying the following question: a tridimensional stable minimal surface is a plane? For this, we need to understand three important facts: in R3 minimal graphics are planes (Bernstein s Theorem), next, minimal surfaces which are graphics of differentiable functions are stables (Theorem of J. L. Barbosa and M. Do Carmo), and finally, we have that the only tridimensional stable complete minimal surfaces are planes (Theorem of M. do Carmo and C. K. Peng)