The Width of Ellipsoids

TL;DR

This paper calculates the k-widths of a round 2-sphere for k=1 to 8 and demonstrates that unstable embedded closed geodesics can occur with multiplicity as min-max critical varifolds.

Contribution

It provides explicit computations of the k-widths of a sphere and links these to the existence of unstable geodesics with multiplicity.

Findings

Computed the k-widths for k=1 to 8 on a 2-sphere.

Showed unstable geodesics can arise with multiplicity.

Connected width computations to min-max theory for geodesics.

Abstract

We compute the $k$-width of a round $2$-sphere for $k=1,\ldots,8$ and we use this result to show that unstable embedded closed geodesics can arise with multiplicity as a min-max critical varifold.