Geometry of positive scalar curvature on complete manifold (Q2082108)

The paper is focused on the geometric analysis of complete, non-compact Riemannian manifolds with positive scalar curvature. The author proves linear volume growth of a complete, non-compact Riemannian 3-manifold with non-negative Ricci curvature and strictly positive scalar curvature. A more general result concerning such Riemannian manifolds of arbitrary dimension is also discussed and a polynomial volume growth is derived. For 3-manifolds of the aforementioned type an upper bound for the width of the manifold is obtained. This result shows that such type 3-manifolds look like 1-dimensional (lines) in the large scale. The approach applied to prove the main results is based on the stability of the geodesic ray, the geometrically relative Bochner formula, and the Lipschitz structure of positive scalar curvature. The paper will be of interest for experts in geometric analysis or differential geometry.