A multiplicity estimate for the Jacobi operator of a nonflat Yang-Mills field over $\mathbb{S}^m$

TL;DR

This paper refines stability results for Yang-Mills fields and harmonic maps, providing improved estimates and implications for Morse index, enhancing understanding of their geometric properties.

Contribution

It offers new refinements of stability results for Yang-Mills fields and harmonic maps, extending previous Morse index estimates.

Findings

Refined stability results for Yang-Mills fields.

Enhanced Morse index estimates for harmonic maps.

Implications for geometric analysis of nonflat fields.

Abstract

Here we provide refinements of the stability results of Simons and Xin, concerning the stability of Yang-Mills fields and harmonic maps respectively. The result also implies the earlier Morse index estimates for both cases.