$\rm{G}_2$-单极子的渐近几何
微分几何
2022-09-13 v4 数学物理
偏微分方程分析
math.MP
摘要
本文研究-单极子的渐近性质。首先，我们证明当底层的-流形是非抛物的（即容许正Green函数）时，具有有界曲率的有限中间能量单极子具有有限质量。第二个主要结果限制于底层-流形为渐近锥形的情形。在此情形下，我们推导出尖锐的衰减估计，并且连接沿端部收敛到渐近锥上的伪Hermitian--Yang--Mills连接。最后，我们的最后一个结果给出了描述渐近锥形-流形上有限中间能量单极子模空间的Fredholm框架。
引用
@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}
}
备注
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