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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Chern-Osserman inequality
for minimal surfaces in H$^{n}$


Authors: Chen Qing and Cheng Yi
Journal: Proc. Amer. Math. Soc. 128 (2000), 2445-2450
MSC (1991): Primary 53A20; Secondary 53C42
Published electronically: December 7, 1999
MathSciNet review: 1664325
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Abstract: We obtain Chern-Osserman's inequality of a complete properly immersed minimal surface in hyperbolic $n$-space, provided the $L^{2}$-norm of the second fundamental form of the surface is finite.


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Additional Information

Chen Qing
Affiliation: Department of Mathematics, The University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: qchen@ustc.edu.cn

Cheng Yi
Affiliation: Department of Mathematics, The University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: chengy@ustc.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05334-4
PII: S 0002-9939(99)05334-4
Keywords: Minimal surface, Chern-Osserman inequality, Euler characteristic
Received by editor(s): September 14, 1998
Published electronically: December 7, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society