# On free boundary minimal surfaces in the Riemannian Schwarzschild manifold

## TL;DR

This paper investigates the existence and properties of free boundary minimal surfaces in the Riemannian Schwarzschild manifold, providing evidence for unbounded minimal surfaces as limits of solutions to a mountain pass problem.

## Contribution

It analyzes the Morse index of minimal surfaces in Schwarzschild space and relates boundary length to density at infinity for free-boundary minimal surfaces.

## Key findings

- The simplest minimal surface has Morse index one.
- Established a relationship between boundary length and density at infinity.
- Provided evidence supporting the existence of unbounded minimal surfaces.

## Abstract

Is it possible to obtain unbounded minimal surfaces in certain asymptotically flat 3-manifolds as a limit of solutions to a natural mountain pass problem with diverging boundaries? In this work, we give evidence that this might be true by analyzing related aspects in the case of the exact Riemannian Schwarzschild manifold. More precisely, we observe that the simplest minimal surface in this space has Morse index one. We prove also a relationship between the length of the boundary and the density at infinity of general minimal surfaces satisfying a free-boundary condition along the horizon.