Abstract In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, prove minimal volume growth, an estimate integral width. higher-dimensional obtain growth stronger condition.

We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric positive scalar curvature, and use it to survey mathematical work employed address Gromov’s observation manifolds with curvature tend be inessential by focusing on four-dimensional case. also point out an strengthening result Carr its extension non-orientable realm.

Let $M_\Sigma$ be an $n$-dimensional Thom-Mather stratified space of depth $1$. We denote by $\beta M$ the singular locus and $L$ associated link. In this paper we study problem when such a can endowed with wedge metric positive scalar curvature. relate to recent work on index theory spaces, giving first obstruction existence in terms $\alpha$-class $\alpha_w (M_\Sigma)\in KO_n$. order establis...