The asymptotic geometry of $\rm G_2$-monopoles

Daniel Fadel, Ákos Nagy, Gonçalo Oliveira

Published 2020-09-14Version 1

This article investigates the asymptotics of $\rm G_2$-monopoles. First, we find that when the underlying $\rm G_2$-manifold has polynomial volume growth strictly greater than $r^{7/2}$, finite intermediate energy monopoles with bounded curvature have finite mass. The second main result restricts to the case when the underlying $\rm G_2$-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 over the asymptotic cone.