Metric Inequalities with Scalar Curvature

TL;DR

This paper derives new inequalities relating to manifolds with positive scalar curvature, extending classical geometric bounds and providing insights into the structure of such manifolds.

Contribution

It introduces novel inequalities for scalar curvature bounds, generalizing classical results on conjugate points in curved surfaces.

Findings

New inequalities for manifolds with positive scalar curvature

Extensions of classical bounds on conjugate points

Insights into geometric structure under scalar curvature constraints

Abstract

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces with positive sectional curvature.