Classificação de hipersuperfícies de fronteira livre em uma classe de domínios conformes à domínios euclidianos

Abstract

In this thesis we explored the compact, orientable and CMC free boundary submanifolds (...) with (...), where (...) is a euclidean ball (...) or an annulus (...), where p is a smooth radial function in (...). Thus, we obtain several classification results in three cases: 1. (...), where (...) denotes the three dimensional euclidean ball of unit radius. 2. (...), where (...) is a minimal submanifold, 3. (...), where (...) is a minimal hypersurface. In the above items we show that under appropriated pinching condition in the second fundamental form of the immersion, or in umbilicity tensor to first case, the submanifolds are of determined topological types and in some cases, we obtain rigidity, is that, we can obtain more geometric properties.