A parametrized compactness theorem under bounded Ricci curvature

Abstract

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

arXiv comment17 pages. Final version to appear in Front. Math. China. Reformulation of Theorem B to Corollary 1, adding some remarks, changing the precompactness in Corollary 1.3 (now Corollary 2) to $C^{0,\alpha }$-norm, and correcting some typos

References in corpus (1)

• Perelman's Stability Theorem