Teorema de Bersntein para gráficos mínimos em R^n, (3,<=n,,=6)

Abstract

The classic Bernstein theorem says that, if a function u : R2 ! R is anentire solution to the minimal surface equationdiv ru p1 + jruj2!= 0then u is a linear function, that is, the graph of u is necessarily a plan. Ifwe consider u : Rn1 ! R, a version of this theorem remains valid untiln 8, counter-examples were found in higher dimensions. Our main goal in this work is to show that this theorem is true for n 6. We will also show that if a hypersurface in the euclidean space is complete, minimal, stable and parabolic then it is necessarily a plan.