The moduli space of embedded singly periodic maximal surfaces with isolated singularities in the Lorentz–Minkowski space \(\mathbb{L}^3\)

1. Bartnik R. and Simon L. (1982/83). Spacelike hypersurfaces with prescribed boundary values and mean curvature. Comm. Math. Phys. 87: 131–152

   Article  MathSciNet  Google Scholar 

2. Calabi E. (1970). Examples of the Bernstein problem for some nonlinear equations. Proc. Symp. Pure Math. 15: 223–230

   MathSciNet  Google Scholar 

3. Cheng S.Y. and Yau S.T. (1976). Maximal space-like hypersurfaces in the Lorentz–Minkowski spaces. Ann. Math. 104(2): 407–419

   MathSciNet  Google Scholar 

4. Ecker K. (1986). Area maximizing hypersurfaces in Minkowski space having an isolated singularity. Manuscr. Math. 56: 375–397

   Article  MATH  MathSciNet  Google Scholar 

5. Estudillo F.J.M. and Romero A. (1992). Generalized maximal surfaces in the Lorentz–Minkowski space \(\mathbb{L}^3\) Math. Proc. Camb. Phil. Soc. 111: 515–524

   MATH  MathSciNet  Google Scholar 

6. Farkas H.M. and Kra I. (1980). Riemann surfaces Graduate Texts in Math., vol. 72. Springer, Berlin

   Google Scholar 

7. Fernández, I., López, F.J.: Periodic Maximal surfaces in the Lorentz–Minkowski space \(\mathbb{L}^3\) (preprint)

8. Fernández I., López F.J. and Souam R. (2005). The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz–Minkowski space \(\mathbb{L}^3\) Math. Ann. 332: 605–643

   Article  MATH  MathSciNet  Google Scholar 

9. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer, Heidelberg (1977)

10. Pérez J. (1997). On singly periodic minimal surfaces with planar ends. Trans. Am. Math. Soc. 349(6): 2371–2389

    Article  MATH  Google Scholar 

11. Klyachin, A.A.: Description of a set of entire solutions with singularities of the equation of maximal surfaces. Math. Sb. (Russian) 194(7), 83–104 (2003); translation in Sb. Math. 194(7–8), 1035–1054 (2003)

12. Klyachin V.A. and Miklyukov V.M. (2003). Geometric structures of tubes and bands of zero mean curvature in Minkowski space. Ann. Acad. Sci. Fenn. Math. 28: 239–270

    MATH  MathSciNet  Google Scholar 

13. Kobayashi O. (1984). Maximal surfaces with conelike singularities. J. Math. Soc. Jpn. 36(4): 609–617

    Article  MATH  Google Scholar 

14. López F.J., López R. and Souam R. (2000). Maximal surfaces of Riemann type in Lorentz–Minkowski space \(\mathbb{L}^3\) Mich. J. Math. 47: 469–497

    Article  MATH  Google Scholar 

15. Umehara M. and Yamada K. (2006). Maximal surfaces with singularities in Minkowski space. Hokkaido Math. J. 35(1): 13–40

    MATH  MathSciNet  Google Scholar 

16. Wolf J. (1967). Spaces of Constant curvature. McGraw-Hill, New York

    MATH  Google Scholar 

17. O’Neill B. (1983). Semmi-Riemannian Geometry. Academic, New York

    Google Scholar 

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