Hipersuperfícies imersas em Hn+1(-1) com curvatura média constante e bordo planar

Abstract

In this work, we present two results that establish sufficient conditions for a manifold to "inherit" the symmetries of its boundary. One involves an immersion with constant mean curvature, Mn+1(c), whose boundary is a closed, embedded (n-1)-dimensional gamma submanifold of M. The other involves a compact hypersurface, Mn, embedded in Hn+1(-l), with non-zero constant mean curvature h. This will be demonstrated by adapting the flux formula to hyperbolic space, as well as theorems stated by Brito et al. (1991). Furthermore, we make use of the Alexandrov reflection principle, as described in Alexandrov (1962).