Chern-Osserman inequality for minimal surfaces in $\mathbf {H}^n$
HTML articles powered by AMS MathViewer
- by Chen Qing and Cheng Yi PDF
- Proc. Amer. Math. Soc. 128 (2000), 2445-2450 Request permission
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
- Michael T. Anderson, Complete minimal varieties in hyperbolic space, Invent. Math. 69 (1982), no. 3, 477–494. MR 679768, DOI 10.1007/BF01389365
- Shiing-shen Chern and Robert Osserman, Complete minimal surfaces in euclidean $n$-space, J. Analyse Math. 19 (1967), 15–34. MR 226514, DOI 10.1007/BF02788707
- Luquésio P. Jorge and William H. Meeks III, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology 22 (1983), no. 2, 203–221. MR 683761, DOI 10.1016/0040-9383(83)90032-0
- Masatoshi Kokubu, Weierstrass representation for minimal surfaces in hyperbolic space, Tohoku Math. J. (2) 49 (1997), no. 3, 367–377. MR 1464184, DOI 10.2748/tmj/1178225110
- Geraldo de Oliveira Filho, Compactification of minimal submanifolds of hyperbolic space, Comm. Anal. Geom. 1 (1993), no. 1, 1–29. MR 1230271, DOI 10.4310/CAG.1993.v1.n1.a1
- Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. MR 0256278
- Leon Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983. MR 756417
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
- Received by editor(s): September 14, 1998
- Published electronically: December 7, 1999
- Communicated by: Christopher Croke
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1664325