论文标题
Riemannian流形的几乎非负标态曲率与Tori一致
Almost non-negative scalar curvature on Riemannian manifolds conformal to tori
论文作者
论文摘要
在本文中，我们通过Yamabe问题将标态圆环定理的几何稳定性猜想降低为共形案例。然后，我们能够证明一系列riemannian歧管序列与均匀控制的扁平托里序列并满足几何稳定性猜想的情况。我们还能够处理一系列riemannian歧管序列与恒定负标态曲率riemannian歧管序列相吻合的情况。还讨论了从共形角度来看的全部猜想，作为解决猜想的可能方法。
In this article we reduce the geometric stability conjecture for the scalar torus rigidity theorem to the conformal case via the Yamabe problem. Then we are able to prove the case where a sequence of Riemannian manifolds is conformal to a uniformly controlled sequence of flat tori and satisfies the geometric stability conjecture. We are also able to handle the case where a sequence of Riemannian manifolds is conformal to a sequence of constant negative scalar curvature Riemannian manifolds which converge to a flat torus in $C^1$. The full conjecture from the conformal perspective is also discussed as a possible approach to resolving the conjecture.
