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.

17 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 $C^{0,α}$-norm, and correcting some typos