Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

A family of maximal surfaces in Lorentz-Minkowski three-space

Authors: Young Wook Kim and Seong-Deog Yang
Journal: Proc. Amer. Math. Soc. 134 (2006), 3379-3390
MSC (2000): Primary 53A10, 53C50
Posted: May 8, 2006
MathSciNet review: 2231923
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence of an infinite family of complete spacelike maximal surfaces with singularities in Lorentz-Minkowski three-space and study their properties. These surfaces are distinguished by their number of handles and have two elliptic catenoidal ends.

References

1. Luis J. Alías, Rosa M. B. Chaves, and Pablo Mira, Björling problem for maximal surfaces in Lorentz-Minkowski space, Math. Proc. Camb. Phil. Soc., 134 (2003), 289-316. MR 1972140 (2004d:53076)
2. E. Calabi, Examples of Bernstein problems for some nonlinear equations, Proc. Symp. Pure Math., 15 (1970), 223-230. MR 0264210 (41:8806)
3. S.-Y. Cheng and S.-T. Yau, Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces, Ann. of Math., 104 (1976), 407-419. MR 0431061 (55:4063)
4. F. J. M. Estudillo and A. Romero, Generalized maximal surfaces in Lorentz-Minkowski space $\mathbb{L}^3$ , Math. Proc. Camb. Phil. Soc., 111 (1992), 515-524. MR 1151327 (93b:53010)
5. I. Fernández and F. López, Periodic maximal surfaces in the Lorentz-Minkowski space $\mathbb{L}^3$ , arXiv:math.DG/0412461 v3.
6. I. Fernández, F. López and R. Souam, The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz-Minkowski space $\mathbb{L}^3$ , arXiv:math.DG/0311330 v2.
7. I. Fernández, F. López and R. Souam, The moduli space of embedded singly periodic maximal surfaces with isolated singularities in the Lorentz-Minkowski space $\mathbb{L}^3$ , arXiv:math.DG/0412190 v1.
8. S. Fujimori, K. Saji, M. Umehara, K. Yamada, Cuspidal crosscaps and singularities of maximal surfaces, Preprint.
9. D. Hoffman and W. H. Meeks III, Embedded minimal surfaces of finite topology, Ann. of Math., 131 (1990), 1-34. MR 1038356 (91i:53010)
10. T. Imaizumi, Maximal surfaces with conelike singularities of finite type, Kobe J. Math., 18 (2001), 51-60. MR 1868796 (2003c:53014)
11. T. Imaizumi, Maximal surfaces with simple ends, Kyushu J. Math., 58 (2004), 59-70. MR 2053719 (2005a:53010)
12. O. Kobayashi, Maximal surfaces in the 3-dimensional Minkowski space , Tokyo J. Math., 6 (1983), 297-309. MR 0732085 (85d:53003)
13. O. Kobayashi, Maximal surfaces with conelike singularities, J. Math. Soc. Japan, 36 (1984), 609-617. MR 0759417 (86d:53008)
14. F. J. López, R. López, and R. Souam, Maximal surfaces of Riemann type in Lorentz-Minkowski space $\mathbb{L}^3$ , Michigan J. of Math., 47 (2000), 469-497. MR 1813540 (2002c:53009)
15. W. Rossman and K. Sato, Constant mean curvature surfaces with two ends in hyperbolic space, Experimental Math., 7, no. 2 (1998), 101-119. MR 1677103 (2000b:53014)
16. R. Schoen, Uniqueness, symmetry, and embeddeness of minimal surfaces, J. Diff. Geom., 18 (1983), 731-809. MR 0730928 (85f:53011)
17. M. Umehara and K. Yamada, Maximal surfaces with singularities in Minkowski space, arXiv:math.DG/0307309 v6; to appear in Hokkaido Mathematical Journal.
18. S.-D. Yang, Elliptic catenoids in $\mathbb{L}^3$ with an arbitrary number of handles, Proceedings of the International Workshop on Integral Systems, Geometry, and Visualization, Nov. 2004, Kyushu University, Fukuoka, Japan.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|