2015/06/10 by Ahmad Afuni, Afuni, Ahmad
Mathematics · Physics and Astronomy · #35B45 #35B53 #53C07 #58E15 #58E20 #70S10 #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #math-ph #math.AP #math.DG #math.MP #msc:35B45 #msc:35B53 #msc:53C07 #msc:58E15 #msc:58E20 #msc:70S10
paper · pdf · doi:10.48550/arxiv.1506.03439
14 pages
arxiv created 2015/06/10 · openalex publication_date 2015/06/10 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate monotonicity properties of p-harmonic vector bundle-valued k-forms by studying the energy-momentum tensor associated with such a form. As a consequence, we obtain a unified proof of the monotonicity formulæ for p-harmonic maps and Yang-Mills connections, proving a monotonicity formula for p-Yang-Mills connections in the process. Moreover, it is shown how this technique may be adapted to yield an analogous monotonicity formula for Yang-Mills-Higgs pairs. Finally, we obtain Liouville-type theorems for such forms and Yang-Mills-Higgs pairs as an application.