论文标题
$ g_2 $ -manifolds上的迭代崩溃现象
Iterated collapsing phenomenon on $G_2$-manifolds
论文作者
论文摘要
我们提出了一种新的折叠机制，用于$ g_2 $ -metrics，通用区域在Riemann表面上接纳了K3纤维上的圆形束结构。绝热描述涉及最大submanifold方程的加权版本。在本地平滑的环境中，我们证明了正式的电源系列解决方案的存在，并在启发式层面上讨论了压实问题。还讨论了$ spin（7）$模拟。
We propose a new collapsing mechanism for $G_2$-metrics, with the generic region admitting a circle bundle structure over a K3 fibration over a Riemann surface. The adiabatic description involves a weighted version of the maximal submanifold equation. In a local smooth setting we prove the existence of formal power series solutions, and the problem of compactification is discussed at a heuristic level. The $Spin(7)$ analogue is also discussed.
