Smoothing Riemannian Metrics with Ricci Curvature Bounds

TL;DR

This paper demonstrates that Riemannian metrics with Ricci curvature and conjugate radius bounds can be smoothed to sectional curvature bounds, leading to new insights into the structure of manifolds with Ricci bounds.

Contribution

It introduces a method to smooth metrics with Ricci bounds to sectional bounds, enabling new geometric and topological results.

Findings

Metrics with Ricci and conjugate radius bounds can be smoothed to sectional curvature bounds.

New structural results about manifolds with Ricci curvature bounds are derived.

The smoothing technique broadens understanding of geometric properties under Ricci constraints.

Abstract

We prove that Riemannian metrics with an absolute Ricci curvature bound and a conjugate radius bound can be smoothed to having a sectional curvature bound. Using this we derive a number of results about structures of manifolds with Ricci curvature bounds.