J. Gu

activity

20102019

most citedAn Optimal Differentiable Sphere Theorem for Complete Manifolds

2 citations · 3 across the 6 of their papers we have counts for

collaborators

7 papers

math.DG2019

The topological rigidity theorem for submanifolds in space forms

Juanru Gu, Hongwei Xu

Let $M$ be an $n (\geq 4)$ -dimensional compact submanifold in the simply connected space form $F^{n + p} (c)$ with constant curvature $c \geq 0$ , where $H$ is the mean curvature of $M$ .…

math.DG2018

A new gap for complete hypersurfaces with constant mean curvature in space forms

Juanru Gu, Li Lei, Hongwei Xu

Let $M$ be an $n$ -dimensional closed hypersurface with constant mean curvature and constant scalar curvature in an unit sphere. Denote by $H$ and $S$ the mean curvature and the squ…

math.DG2011

Topological and differentiable rigidity of submanifolds in space forms

Hong-Wei Xu, Juan-Ru Gu

Let $F^{n + p} (c)$ be an $(n + p)$ -dimensional simply connected space form with nonnegative constant curvature $c$ . We prove that if $M^{n} (n \geq 4)$ is a compact submanifold in $F^{n+p}(…

math.DG2011

Rigidity of submanifolds with parallel mean curvature in space froms

Hong-Wei Xu, Juan-Ru Gu

Let $M$ be an $n (\geq 3)$ -dimensional oriented compact submanifold with parallel mean curvature in the simply connected space form $F^{n + p} (c)$ with $c + H^{2} > 0$ , where $H$ is the mean…

math.DG2011★ 1 cited

On Yau rigidity theorem for minimal submanifolds in spheres

Juan-Ru Gu, Hong-Wei Xu

In this note, we investigate the well-known Yau rigidity theorem for minimal submanifolds in spheres. Using the parameter method of Yau and the DDVV inequality verified by Lu, Ge a…

math.DG2011

The sphere theorems for manifolds with positive scalar curvature

Juan-Ru Gu, Hong-Wei Xu

Some new differentiable sphere theorems are obtained via the Ricci flow and stable currents. We prove that if $M^{n}$ is a compact manifold whose normalized scalar curvature and sect…