# A global bound for the singular set of area-minimizing hypersurfaces

## TL;DR

This paper establishes a universal bound on the size of the singular set of area-minimizing hypersurfaces based on boundary geometry, advancing understanding of their regularity properties.

## Contribution

It provides the first a priori measure bound for the singular set of area-minimizing hypersurfaces in relation to boundary geometry.

## Key findings

- Bound on (n-7)-dimensional measure of singular set
- Relation between boundary geometry and singular set size
- Improved regularity estimates for hypersurfaces

## Abstract

We give an a priori bound on the (n-7)-dimensional measure of the singular set for an area-minimizing n-dimensional hypersurface, in terms of the geometry of its boundary.