The p-widths of the Hemisphere

TL;DR

This paper calculates the p-widths for the hemisphere with the standard metric, providing the first example of a manifold with boundary where all p-widths are explicitly known.

Contribution

It introduces the first explicit computation of p-widths for a manifold with boundary, specifically the hemisphere, for all p.

Findings

Explicit p-widths for the hemisphere are obtained.

First example with known p-widths for all p on a manifold with boundary.

Advances understanding of geometric widths in boundary manifolds.

Abstract

We compute the p-widths, $\{\omega_p\}$, for the hemisphere with the standard round metric. This provides the first example of a manifold with boundary for which the $p$-widths are known for all $p$.