Journal of the Ramanujan Mathematical Society

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Existence of Maximal Surface Containing Given Curve and Special Singularity


Affiliations
1 International Centre for Theoretical Sciences, Bengaluru - 560089, India
2 Department of Mathematics, Shiv Nadar University, Dadri 201314, Uttar Pradesh, India
3 Department of Mathematics, Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, Uttar Pradesh, India
     

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We give a different formulation for describing maximal surfaces in Lorentz-Minkowski space, ๐•ƒ3, using the identification of ๐•ƒ3 with โ„‚ร—โ„. Further we give a different proof for the singular Bjorling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surface which contains a given curve and has a special singularity.
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  • J. A. Aledo, J. A. Galvez and P. Mira, Bjorling representation for spacelike surfaces with H = cK in L3, Proceedings of the II International Meeting on Lorentzian Geometry, Publ. de la RSME, 8 (2004) 2โ€“7.

  • L. J. Alias, R. M. B. Chaves and P. Mira, Bjorling problem for maximal surfaces in Lorentz-Minkowski space, Math. Proc. Cambridge Philos. Soc., 134 (2003) no. 2, 289โ€“316.

  • F. J. M. Estudillo and A. Romero, Generalized maximal surfaces in LorentzMinkowski space L3, Math. Proc. Cambridge Philos. Soc., 111 (1992) no. 3, 515โ€“524.

  • I. Fernandez, F. Lopez and R. Souam, The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz-Minkowski space L3, Math. Ann., 332(3) (2005) 605โ€“643.

  • S. Fujimori, K. Saji, M. Umehara and K. Yamada, Singularities of maximal surfaces, Math. Z., 259 (2008) 827โ€“848.

  • T. Iwaniec, L. V. Kovalev and J. Onninen, Doubly connected minimal surfaces and extremal harmonic mappings, J. Geom Anal., 22 (2012) 726โ€“762.

  • Y. W. Kim and S.-D. Yang, A family of maximal surfaces in Lorentz-Minkowski three-space, Proc. Amer. Math. Soc., 134 (2006) 3379โ€“3390.

  • Y. W. Kim and S.-D. Yang, Prescribing singularities of maximal surfaces via a singular Bjorling representation formula, J. Geom. Phys., 57 (2007) no. 11, 2167โ€“2177.

  • Y.W. Kim, S.-E. Koh, H. Shin and S.-D. Yang, Spacelike maximal surfaces, timelike minimal surfaces, and Bjorling representation formulae, Journal of Korean Math. Soc., 48 (2011) 1083โ€“1100.

  • O. Kobayashi, Maximal surfaces with conelike singularities, J. Math. Soc., Japan, 36 no. 4, (1984).

  • R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, International Electronic Journal of Geometry, 7 (2014) no. 1, 44โ€“107 .

  • B. Oยด Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York (1983).

  • M. Umehara and K. Yamada, Maximal surfaces with singularities in Minkowski space, Hokkaido Math. J., 35 (2006) 13โ€“40.


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  • Existence of Maximal Surface Containing Given Curve and Special Singularity

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Authors

Rukmini Dey
International Centre for Theoretical Sciences, Bengaluru - 560089, India
Pradip Kumar
Department of Mathematics, Shiv Nadar University, Dadri 201314, Uttar Pradesh, India
Rahul Kumar Singh
Department of Mathematics, Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, Uttar Pradesh, India

Abstract


We give a different formulation for describing maximal surfaces in Lorentz-Minkowski space, ๐•ƒ3, using the identification of ๐•ƒ3 with โ„‚ร—โ„. Further we give a different proof for the singular Bjorling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surface which contains a given curve and has a special singularity.

References