论文标题
具有正标曲率的歧管的度量极限
Metric limits of manifolds with positive scalar curvature
论文作者
论文摘要
我们表明，在$ n \ geq 4 $上符合圆形度量的任何riemannian公制，以$ n \ geq 4 $的形式限制了$ s^n $的riemannian riemannian指标，这是$ s^n $在$ s^n $上的统一意义上的统一融合的意义。特别是，标量曲率的非负性不能在这种限制下保留。
We show that any Riemannian metric conformal to the round metric on $S^n$, for $n\geq 4$, arises as a limit of a sequence of Riemannian metrics of positive scalar curvature on $S^n$ in the sense of uniform convergence of Riemannian distance. In particular, non-negativity of scalar curvature is not preserved under such limits.
