A parametrized compactness theorem under bounded Ricci curvature

TL;DR

This paper establishes a new compactness theorem for manifolds with bounded Ricci curvature, limited diameter, and injectivity radius, advancing understanding of geometric stability under these constraints.

Contribution

It introduces a parametrized compactness theorem specifically for manifolds with bounded Ricci curvature, diameter, and injectivity radius.

Findings

Proves a compactness theorem under specified geometric bounds

Provides conditions for manifold convergence

Enhances understanding of geometric stability

Abstract

We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.