Shicheng Xu

activity

20122026

most citedQuantitative Volume Space Form Rigidity Under Lower Ricci Curvature Bound

24 citations · 59 across the 20 of their papers we have counts for

collaborators

Showing 2019Show all

3 papers · 1 filter

math.DG2019★ 1 cited

1st eigenvalue pinching for convex hypersurfaces in a Riemannian manifold

Yingxiang Hu, Shicheng Xu

Let $M^{n}$ be a closed convex hypersurface lying in a convex ball $B (p, R)$ of the ambient $(n + 1)$ -manifold $N^{n + 1}$ . We prove that, by pinching Heintze-Reilly's inequality via sect…

math.DG2019★ 2 cited

Recognizing shape via 1st eigenvalue, mean curvature and upper curvature bound

Yingxiang Hu, Shicheng Xu

Let $M^{n}$ be a closed immersed hypersurface lying in a contractible ball $B (p, R)$ of the ambient $(n + 1)$ -manifold $N^{n + 1}$ . We prove that, by pinching Heintze-Reilly's inequality…

math.DG2019★ 8 cited

Margulis lemma and Hurewicz fibration Theorem on Alexandrov spaces

Shicheng Xu, Xuchao Yao

We prove the generalized Margulis lemma with a uniform index bound on an Alexandrov $n$ -space $X$ with curvature bounded below, i.e., small loops at $p \in X$ generate a subgroup of…