论文标题
$ 3 $的拓扑，具有均匀积极标量曲率的拓扑
Topology of $3$-manifolds with uniformly positive scalar curvature
论文作者
论文摘要
在本文中，我们对具有均匀积极标态曲率的$ 3 $ manifolds进行了分类。确切地说，我们表明，当且仅当它是（可能是）无限连接的球形$ 3 $ -MANIFOLDS和一些$ \ Mathbb {s} s}^1 \ times \ times \ Mathbb {s}^2 $的$ 3 $ -MANIFOLD和一些副本时，面向$ 3 $ MANIFOLD的完全标量曲率具有完整的指标。此外，我们研究了一个带有平均凸边界的面向$ 3 $ manifold，并且具有均匀的正标曲率。如果边界是封闭表面的不一致结合，则歧管是（可能）无限的球形$ 3 $ manifolds，一些手柄和某些副本的$ \ mathbb {s}^1 \ times \ times \ mathbb {s}^2 $。
In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is homeomorphic to an (possibly) infinite connected sum of spherical $3$-manifolds and some copies of $\mathbb{S}^1\times \mathbb{S}^2$. Further, we study an oriented $3$-manifold with mean convex boundary and with uniformly positive scalar curvature. If the boundary is a disjoint union of closed surfaces, then the manifold is an (possibly) infinite conned sum of spherical $3$-manifolds, some handlebodies and some copies of $\mathbb{S}^1\times \mathbb{S}^2$.
