3 papers
math.DG2026
Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature
Cuifang Si, Shicheng Xu
Let be a sequence of non-collapsed -manifolds with two-sidedly bounded Ricci curvature. We show that the Gromov-Haudorff limit space, , of the associated sequence of or…
math.DG2025
Rigidity for Einstein manifolds under bounded covering geometry
Cuifang Si, Shicheng Xu
In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold must be flat if it is Einstein, i.e. $\opera…
math.DG2025
Precompactness of domains with lower Ricci curvature bound under Gromov-Hausdorff topology
Shicheng Xu
Based on a quantitative version of the classical Hopf-Rinow theorem in terms of the doubling property, we prove new precompactness principles in the (pointed) Gromov-Hausdorff topo…