Uma prova simples do Teorema de Calabi-Bernstein sobre superfícies tipo-espaço máximas

Abstract

The Calabi-Bernstein Theorem, which states that the only entire solutions to the maximal surface equation are affine functions, is a very well known result in Lorentzian Geometry, collecting many different proofs along the years since its original, one due to E. Calabi. In this work, we study a direct and simple proof of this theorem given by A. Romero, aiming to be easily understood by beginning researchers. As such, this proof only requires basic Riemannian and Semi-Riemannian Geometry preliminaries, which have been included in the text, in addition to Liouville Theorem on holomorphic functions of one complex variable.