6 papers
An improved result on Chern conjecture
Qing-Ming Cheng, Fengjiang Li, Guoxin Wei +1
Let be a closed minimal hypersurface with constant scalar curvature. Chern conjecture says that a closed minimal hypersurface with constant scalar cu…
A Classification of Complete Self-shrinkers
Qing-Ming Cheng, Fengjiang Li, Guoxin Wei
Let be an -dimensional complete self-shrinker. We obtain a complete classification of complete self-shrinkers with positive constant scalar curvature. More pr…
Estimates on scalar curvature of self-shrinkers
Qing-Ming Cheng, Fengjiang Li, Guoxin Wei
In this paper, we study -dimensional complete self-shrinkers in with constant squared norm of the second fundamental form. We partially resolve the conject…
Examples of compact embedded mean convex -hypersurfaces
Qing-Ming Cheng, Junqi Lai, Guoxin Wei
There is a well-known conjecture asserts that the round sphere should be the only compact embedded self-shrinker (i.e. -hypersurface) which is diffeomorphic to a sphere. S. Bren…
Complete two-sided -stable minimal hypersurfaces in
Qing-Ming Cheng, Guoxin Wei
In this paper, we study complete -stable minimal hypersurfaces in . We prove that complete two-sided -stable minimal hypersurfaces have Euclidean volume grow…
Embedded cylindrical and doughnut-shaped -hypersurfaces
Qing-Ming Cheng, Junqi Lai, Guoxin Wei
In the paper, we construct, for , complete embedded and non-convex -hypersurfaces, which are diffeomorphic to a cylinder. Hence, one can not expect that -hypersurfaces s…