Geometry of three-dimensional manifolds with positive scalar curvature
Abstract
abstract: 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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Operator Algebra Research
Publication details
- Journal / source
- American Journal of Mathematics
- Publisher
- Project MUSE
- Volume
- 148
- Issue
- 1
- Pages
- 131–160
- Publication date
- 23 January 2026
- Language
- EN