Caracterizações do plano e do catenoide como superfícies capilares à bola euclidiana tridimensional

Abstract

The objective of this work is concerned with obtaining results that allow characterize, in a certain sense, minimal capillary surfaces immersed in the three-dimensional Euclidean ball and wich have the topology of a disk or that of a ring . We will see that a minimum capillary disk to the ball is a flat disk and that a minimum capillary surface at R³\B³ with finite total curvature is a piece of a plane or a piece of a catenoid, where B³ is the Euclidian tridimentional ball of center at origin and radius one.