3 citations · 4 across the 7 of their papers we have counts for
11 papers
Canonical nilpotent structure under bounded Ricci curvature and Reifenberg local covering geometry over regular limits
Zuohai Jiang, Lingling Kong, Shicheng Xu
It is known that a closed collapsed Riemannian -manifold of bounded Ricci curvature and Reifenberg local covering geometry admits a nilpotent structure in the sense of C…
Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound
Lina Chen, Shicheng Xu
The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $…
Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I
Zuohai Jiang, Lingling Kong, Shicheng Xu
We extend Cheeger-Gromov's and Anderson's convergence theorems to regular limit spaces of manifolds with bounded Ricci curvature and local covering geometry, by establishing the $C…
Total squared mean curvature of immersed submanifolds in a negatively curved space
Yanyan Niu, Shicheng Xu
Let and be two integers. Let be an isometrically immersed closed -submanifold of co-dimension that is homotopic to a point in a complete manifold ,…
1st eigenvalue pinching for convex hypersurfaces in a Riemannian manifold
Yingxiang Hu, Shicheng Xu
Let be a closed convex hypersurface lying in a convex ball of the ambient -manifold . We prove that, by pinching Heintze-Reilly's inequality via sect…
Recognizing shape via 1st eigenvalue, mean curvature and upper curvature bound
Yingxiang Hu, Shicheng Xu
Let be a closed immersed hypersurface lying in a contractible ball of the ambient -manifold . We prove that, by pinching Heintze-Reilly's inequality…