科研之友
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摘要
We study a complete noncompact hypersurface M-n isometrically immersed in an (n + 1)-dimensional sphere Sn+1 (n >= 3). We prove that there is no non-trivial L-2-harmonic 2-form on M, if the length of the second fundamental form is less than a fixed constant. We also showed that the same conclusion holds if the scale-invariant total tracefree curvature is bounded above by a small constant depending only on n. These results are generalized versions of the result of Cheng and Zhou on bounded harmonic functions with finite Dirichlet integral and the one of Fang and the author on L-2 harmonic 1-forms.
- 出版日期2015-10-15
- 单位江苏大学; 江苏理工学院
