论文标题
具有正标曲率的三维流形的几何形状
Geometry of three-dimensional manifolds with positive scalar curvature
论文作者
论文摘要
本文的目的是为具有正标曲率的三维完整歧管得出体积和其他几何信息。如果RICCI曲率是非负的，则表明，当标量曲率从下方以正常常数为界时，歧管的体积必须为线性生长。这回答了格罗莫夫（Gromov）的一个问题。对于标量曲率衰减为零的情况，还获得了体积增长估计值。实际上，对于RICCI曲率是渐近的非负率的更一般情况下，建立了类似性质的结果。
The purpose of this paper is to derive volume and other geometric information for three-dimensional complete manifolds with positive scalar curvature. In the case that the Ricci curvature is nonnegative, it is shown that the volume of the manifold must be of linear growth when the scalar curvature is bounded from below by a positive constant. This answers a question of Gromov in the affirmative for dimension three. Volume growth estimates are also obtained for the case when scalar curvature decays to zero. In fact, results of similar nature are established for the more general case that the Ricci curvature is asymptotically nonnegative.
