Work

Stable Abelian Yang--Mills--Higgs Fields on the Round Three-Sphere

Year: 2026

Type: preprint

Abstract: We prove that every stable weak critical point of the self-dual abelian Yang--Mills--Higgs energy on the round three-sphere is gauge equivalent to the vacuum, for every positive scale parameter. This establishes the three-dimensional statement proposed by Cheng. For the non-stable critical point, we give a quantitative upper bound for the lowest eigenvalue of the Hessian on the gauge quotient.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.24045

Author: Jin, Xishen

Institution: Renmin University of China

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Fundamental Research Funds for the Central Universities

OpenAlex ID: W7214006766

Cites: 21

Cited by:

Related to: 10