One of the principal aims of this study is to understand spaces which carry metrics of positive
scalar curvature. In recent years this subject has been the focus of lively research, and we …

arXiv:1908.10612v6 [math.DG] 8 Jul 2021 Page 1 arXiv:1908.10612v6 [math.DG] 8 Jul 2021
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …

Groping our way toward a theory of singular spaces with positive scalar curvatures we look
at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with …

This is a comprehensive presentation of the geometry of submanifolds that expands on
classical results in the theory of curves and surfaces. The geometry of submanifolds starts …

Any smooth manifold can be equipped with a smooth Riemannian metric, that is, a smoothly
varying inner product on each tangent space. A Riemannian metric allows us to do geometry …

Abstract CONTENTS § 1. Introduction Chapter I. Survey of results § 2. Closed spaces of non-
negative curvature § 3. Open spaces of non-negative curvature § 4. Convex sets. Structure …

We show that the combination of non-negative sectional curvature (or 2-intermediate Ricci
curvature) and strict positivity of scalar curvature forces rigidity of complete (non-compact) …

Our main results can be stated as follows:¶¶ 1. For any given numbers m, C and D, the class
of m-dimensional simply connected closed smooth manifolds with finite second homotopy …

Our main theorem asserts that for all odd n≥3 and 0< δ≤1, there exists a small constant,
i(n,δ)>0, such that if a simply connected n-manifold, M, with vanishing second Betti number …

Let M be a closed simply connected manifold and 0< δ≤1. Klingenberg and Sakai
conjectured that there exists a constant i_0=i_0(M,δ)>0 such that the injectivity radius of any …