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

TL;DR

This paper introduces a new family of properly embedded free boundary minimal hypersurfaces with rotational symmetry in Schwarzschild space, answering an open question about their existence in 3D cases.

Contribution

It constructs explicit examples of free boundary minimal hypersurfaces with rotational symmetry in Schwarzschild space, including non-totally geodesic surfaces in 3D.

Findings

Existence of new free boundary minimal hypersurfaces in Schwarzschild space

Construction of hypersurfaces with circular boundaries in the horizon

Answer to the open question by Chodosh and Ketover in 3D case

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, $n\geq3$. In particular, we answer a question proposed by O. Chodosh and D. Ketover \cite{CK} on the existence of non-totally geodesic minimal surfaces in the 3-dimensional Schwarzschild space.