Strong multiplicity one theorems and homological min-max theory

TL;DR

This paper investigates the min-max p-widths of the unit 3-sphere, establishing which lie between specific values, and extends Zhou's multiplicity one theorem with stronger results.

Contribution

It determines specific min-max widths of the 3-sphere and provides stronger versions of Zhou's multiplicity one theorem.

Findings

The 10th to 13th widths of the 3-sphere lie between 2π^2 and 8π.

Stronger versions of Zhou's multiplicity one theorem are proved.

The results clarify the structure of min-max widths in geometric analysis.

Abstract

It was asked by Marques-Neves which min-max $p$-widths of the unit $3$-sphere lie strictly between $2\pi^2$ and $8\pi$. We show that the 10th to the 13th widths do. More generally, we prove stronger versions of X. Zhou's multiplicity one theorem.