# Compactness analysis for free boundary minimal hypersurfaces

## TL;DR

This paper studies the compactness properties of free boundary minimal hypersurfaces in low-dimensional Riemannian manifolds, establishing conditions for convergence and analyzing the behavior of limits, with implications for finiteness and topology.

## Contribution

It introduces geometric conditions guaranteeing strong convergence and analyzes limit behaviors, advancing understanding of free boundary minimal hypersurfaces.

## Key findings

- Conditions for strong one-sheeted graphical convergence
- Analysis of multi-sheeted convergence limits
- Implications for finiteness and topological control

## Abstract

We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control.