arXiv subjects

Cuifang Si

Publications and source records attributed to Cuifang Si.

2 recordsLinked to original sources

arXiv2026

Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature

Let $M_i$ be a sequence of non-collapsed $n$-manifolds with two-sidedly bounded Ricci curvature. We show that the Gromov-Haudorff limit space, $Y$, of the associated sequence of orthonormal frame bundles, $FM_i$, equipped with an almost canonical metric, shares similar properties as a Ricci limit space of non-collapsing sequence i.e., the singular set has codimension $\ge 4$ whose complement contains an open and dense $C^{1,\alpha}$-Riemannian manifold.

math.DG↗

arXiv2024

Rigidity for Einstein manifolds under bounded covering geometry

In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=\lambda g$ for some real number $\lambda$. (2) A compact Einstein manifolds with a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form.

math.DG↗