Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614416 | Journal of Mathematical Analysis and Applications | 2016 | 7 Pages |
Abstract
This paper provides some gap theorems for complete immersed minimal submanifolds of dimension no less than five in a hyperbolic space. Namely, we show that an n(≥5)-dimensional complete immersed minimal submanifold M in a hyperbolic space is totally geodesic if the L2L2 norm of |A||A| on geodesic balls centered at some point p∈Mp∈M has less than quadratic growth and if either supx∈M|A|2(x)supx∈M|A|2(x) is not too large or the LnLn norm of |A||A| on M is small, here, A is the second fundamental form of M.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Changyu Xia, Qiaoling Wang,