Work

The Higher Order Yang–Mills–Higgs Flow Over Riemannian Manifold

Year: 2026

Type: article

Abstract: In this paper, we introduce a novel higher-order Yang–Mills–Higgs functional $\mathcal {YMH}_k(\nabla ,u)$ , which is closely associated with a generalized Higgs-like potential W . First, by employing de Turck’s trick, we establish the local existence of the negative gradient flow, thus refining the ellipticity argument presented in [Car. Var. PDE 58 (2019), 100]. We establish the long-time existence of the flow under conditions on the order of derivatives appearing in the functional and on the degree of the potential W . This result refines and extends the one given in [J. Aust. Math. Soc. 113 (2022), 257-287]. At last, we discuss the physical applications of our higher-order Yang–Mills–Higgs theory and its long-time flow, clarifying the rationale for the higher-order terms and the polynomial potential, rooted in specific mathematical models.

Source: Journal of Nonlinear Mathematical Physics

DOI: 10.1007/s44198-026-00391-z

Authors: Xian-Min Cao, Mehraj Ahmad Lone, Wen Wang, Meng-Jie Zhang, Pan Zhang

Institutions: Anhui University, National Institute of Technology Srinagar, Hefei Normal University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,490

Funder: National Natural Science Foundation of China