Proper free-boundary minimal hypersurfaces with a rotational symmetry in the Schwarzschild space

Abstract

In this work we present a new family of properly embedded free boundary minimal hypersurfaces of revolution with circular boundaries in the horizon of the n-dimensional Schwarzschild space, n ≥ 3. In particular, we answer a question proposed by O. Chodosh and D. Ketover [6] on the existence of non-totally geodesic minimal surfaces in the 3-dimensional Schwarzschild space.