Geometria das superfícies mergulhadas no R3

Abstract

In this work we will make a brief study about mean curvature and surfaces, demonstrating some results and presenting some examples. In addition, the aim of this dissertation is to present a proof of R. Reilly's Alexandrov Theorem. The theorem states The only compact, connected, constant mean curvature hypersurfaces immersed in Euclidean space are the spheres. Alexandrov's theorem was proved by A. D. Alexandrov in the article Uniqueness Theorems for Surfaces in the Large V, published in 1958 by Vestnik Leningrad University, volume 13, number 19, pages 5 to 8. In his demonstration, Alexandrov used the famous Tangency Principle, which he introduced in the above-mentioned article.