论文标题
G_2-拉普拉斯流动中渐近圆锥梯度缩小孤子的独特性
Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G_2-Laplacian Flow
论文作者
论文摘要
对于封闭的G_2结构的拉普拉斯流动，我们证明了渐近圆锥形（AC）梯度缩小的孤子的唯一结果：如果两个梯度缩小到laplacian流向laplacian流量是相同的封闭的G_2-cone渐近的solitons，那么它们的G_2结构是等于solitons的，而G_2结构则是iss的。证明扩展了Kotschwar和Wang的论点，即AC梯度缩小Ricci孤子的独特性。我们还表明，AC收缩端的G_2结构的对称性是从其渐近锥中继承的。在对基本组的温和假设下，渐近锥的对称性扩展到全局对称性。
We prove a uniqueness result for asymptotically conical (AC) gradient shrinking solitons for the Laplacian flow of closed G_2-structures: If two gradient shrinking solitons to Laplacian flow are asymptotic to the same closed G_2-cone, then their G_2-structures are equivalent, and in particular, the two solitons are isometric. The proof extends Kotschwar and Wang's argument for uniqueness of AC gradient shrinking Ricci solitons. We additionally show that the symmetries of the G_2-structure of an AC shrinker end are inherited from its asymptotic cone; under a mild assumption on the fundamental group, the symmetries of the asymptotic cone extend to global symmetries.
