The asymptotic geometry of $\rm{G}_2$-monopoles
Abstract
This article investigates the asymptotics of -monopoles. First, we prove that when the underlying -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 -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 -manifold.
Keywords
Cite
@article{arxiv.2009.06788,
title = {The asymptotic geometry of $\rm{G}_2$-monopoles},
author = {Daniel Fadel and Ákos Nagy and Gonçalo Oliveira},
journal= {arXiv preprint arXiv:2009.06788},
year = {2022}
}
Comments
83 pages. v4: Corrected minor mistakes/typos on the Bochner--Weitzenb\"ock formulas of Lemmas 5.2, 5.3, 5.5 and 9.1. In particular, this led to a restatement of both Corollary 5.4 and Proposition 6.3, and their proofs were rewritten. Final version to appear in the Memoirs of the American Mathematical Society