Width Stability of Rotationally Symmetric Metrics

TL;DR

This paper proves a conjecture regarding the stability of the min-max width of three-spheres under rotational symmetry, extending the results to all dimensions n≥3, advancing understanding in geometric analysis.

Contribution

It establishes the stability of the min-max width for rotationally symmetric metrics on spheres, confirming a conjecture and generalizing to higher dimensions.

Findings

Proved the Marques-Neves conjecture on width stability.

Extended stability results to all dimensions n≥3.

Validated alternative formulations of the conjecture.

Abstract

We prove a conjecture of Marques-Neves in arXiv:2103.10093, and several alternative formulations thereof, about the stability of the min-max width of three-spheres under the additional assumption of rotational symmetry. We can moreover extend our results to all dimensions $n\geqslant 3$.