论文标题
$ \ rm {g} _2 $ - 单孔的渐近几何形状
The asymptotic geometry of $\rm{G}_2$-monopoles
论文作者
论文摘要
本文调查了$ \ rm {g} _2 $ - 单极的渐近学。首先，我们证明，当基本的$ \ rm {g} _2 $ -Manifold是非核子（即接受正绿色的功能）时，有限的中间能量单极具有有限的曲率质量。第二个主要结果限制在基础$ \ rm {g} _2 $ -Manifold是渐近的圆锥形时。在这种情况下，我们推断出尖锐的衰减估计值，并且连接沿着末端将伪锥的伪式 - 千磨 - 毫无用处的连接收敛。最后，我们的最后结果展示了弗雷德姆设置，描述了有限的中间能量单孔在渐近圆锥形$ \ rm {g} _2 $ -Manifold上的模量空间。
This article investigates the asymptotics of $\rm{G}_2$-monopoles. First, we prove that when the underlying $\rm{G}_2$-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 $\rm{G}_2$-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 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 $\rm{G}_2$-manifold.
