Alguns resultados de rigidez em superfícies mínimas Free Boundary

Abstract

In this work, we study some rigidity theorems for free boundary minimal surfaces. Firstly, we have studied a foliation result by free boundary surfaces of constant mean curvature and, through this, we have approached a global rigidity result for mean convex three-dimensional manifolds. This result was proved by L. Ambrozio [1]. After this, we study a rigidity result for free-boundary minimal surfaces immersed in the three-dimensional ball, since a pinching condition on the norm of the second fundamental form. In this context, we obtain the important examples of the fat equatorial disc and the critical catenoid. This result was addressed by L. Ambrozio and I. Nunes [3].