The asymptotic geometry of \rmG₂-monopoles

2020/09/14 by Fadel, Daniel, Nagy, Ákos, Oliveira, Gonçalo · 1 citation
#53C07 #58D27 #58E15 #70S15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2009.06788

Abstract

This article investigates the asymptotics of \rmG₂-monopoles. First, we prove that when the underlying \rmG₂-manifold is nonparabolic (i.e. admits a positive Green's function), finite intermediate energy monopoles with bounded curvature have finite mass. The second main result restricts to the case when the underlying \rmG₂-manifold is asymptotically conical. In this situation, we deduce sharp decay estimates and that the connection converges, along the end, to a pseudo-Hermitian--Yang--Mills connection over the asymptotic cone. Finally, our last result exhibits a Fredholm setup describing the moduli space of finite intermediate energy monopoles on an asymptotically conical \rmG₂-manifold.

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