论文标题
具有非负标态曲率的完整歧管的刚度结果
Rigidity results for complete manifolds with nonnegative scalar curvature
论文作者
论文摘要
在本文中，我们将显示一些具有非负标态曲率的完全开放的Riemannian歧管的刚度结果。在不使用著名的Cheeger-gromoll分裂定理的情况下，我们为具有非负标量曲率的完整歧管提供了新的证明，该曲率符合非零度的适当平滑映射到$ t^{n-1} \ times \ Mathbf R $具有非零度。在这里，我们引入了一种技巧，可以从局部图形收敛中获得极限性超表面的紧凑性。基于同一想法，我们还为几类具有积极标态曲率的完整riemannian流形的类别建立了最佳的$ 2 $ - 总结不平等，并进一步证明了平等案例的刚性结果。
In this paper, we are going to show some rigidity results for complete open Riemannian manifolds with nonnegative scalar curvature. Without using the famous Cheeger-Gromoll splitting theorem we give a new proof to a rigidity result for complete manifolds with nonnegative scalar curvature admitting a proper smooth map to $T^{n-1}\times \mathbf R$ with nonzero degree. Here we introduce a trick to obtain the compactness of limit hypersurface from locally graphical convergence. Based on the same idea we also establish an optimal $2$-systole inequality for several classes of complete Riemannian manifolds with positive scalar curvature and further prove a rigidity result for the equality case.
