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Rigidity of minimal submanifolds in hyperbolic space

Authors
Seo, Keomkyo
Issue Date
Feb-2010
Publisher
BIRKHAUSER VERLAG AG
Keywords
Minimal submanifold; Total scalar curvature; Hyperbolic space; L(2) Harmonic 1-form
Citation
ARCHIV DER MATHEMATIK, v.94, no.2, pp.173 - 181
Journal Title
ARCHIV DER MATHEMATIK
Volume
94
Number
2
Start Page
173
End Page
181
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/13279
DOI
10.1007/s00013-009-0096-2
ISSN
0003-889X
Abstract
We prove that if an n-dimensional complete minimal submanifold M in hyperbolic space has sufficiently small total scalar curvature then M has only one end. We also prove that for such M there exist no nontrivial L (2) harmonic 1-forms on M.
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