Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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
     

   Subscribe/Renew Journal


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.
User
Subscription Login to verify subscription
Notifications
Font Size

  • 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.


Abstract Views: 262

PDF Views: 1




  • Existence of Maximal Surface Containing Given Curve and Special Singularity

Abstract Views: 262  |  PDF Views: 1

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