# A hardness of approximation result in metric geometry

## TL;DR

This paper proves that approximating the hyperspherical radius of a triangulated manifold within nearly polynomial factors is NP-hard, highlighting computational complexity challenges in metric geometry.

## Contribution

It establishes a new NP-hardness result for approximating the hyperspherical radius in metric geometry, a problem previously not well-understood in terms of computational difficulty.

## Key findings

- NP-hardness of approximation within almost-polynomial factors
- Highlights computational complexity in metric geometry problems
- Provides theoretical bounds for approximation difficulty

## Abstract

We show that it is $\mathsf{NP}$-hard to approximate the hyperspherical radius of a triangulated manifold up to an almost-polynomial factor.