# Minimal hypersurfaces with arbitrarily large area

## TL;DR

This paper proves that in certain high-dimensional Riemannian manifolds, there exist sequences of minimal surfaces with arbitrarily large areas, expanding understanding of minimal hypersurfaces in geometric analysis.

## Contribution

It establishes the existence of unbounded-area minimal hypersurfaces in bumpy closed Riemannian manifolds for dimensions 3 to 7, a significant advancement in geometric measure theory.

## Key findings

- Existence of sequences of minimal hypersurfaces with unbounded area
- Applicable for dimensions 3 to 7
- Advances understanding of minimal surface theory in high dimensions

## Abstract

For 3 $\leq$ n $\leq$ 7, we prove that a bumpy closed Riemannian n-manifold contains a sequence of connected embedded closed minimal surfaces with unbounded area.