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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
DOI: https://doi.org/10.1090/S0002-9939-99-05334-4
Published electronically: December 7, 1999
MathSciNet review: 1664325
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. M. T. Anderson, Complete minimal varieties in hyperbolic space, Invent.math. 69 (1982), 477-494. MR 84c:53005
  • 2. S. S. Chern and R. Osserman, Complete minimal surface in $E^{N}$, J. d'Analyse Math. 19 (1967), 15-34. MR 37:2103
  • 3. L. P. Jorge and W. H. Meeks, The topology of minimal surfaces of finite total Gaussian curvature, Topology 22 (1983), 203-221. MR 84d:53006
  • 4. M. Kokubu, Weierstrass representation for minimal surfaces in hyperbolic space, Tohoku Math. J. 49 (1997), 367-377. MR 98f:53008
  • 5. G. De Oliveira, Compactification of minimal submanifolds of hyperbolic space, Comm. An. and Geom. 1 (1993), 1-29. MR 94h:53080
  • 6. R. Osserman, A survey of minimal surfaces, Van Norstrand Rienhold,New York, 1969. MR 41:934
  • 7. L. Simon, Lectures on Geometric Measure Theory, C.M.A. Australian National University Vol.3, 1983. MR 87a:49001

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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: https://doi.org/10.1090/S0002-9939-99-05334-4
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

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