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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 2, Pages 5–20 (Mi izv425)  

This article is cited in 14 scientific papers (total in 14 papers)

Zero mean curvature surfaces of mixed type in Minkowski space

V. A. Klyachin

Volgograd State Pedagogical University

Abstract: We investigate zero mean curvature surfaces in the Minkowski space ${\mathbb R}^3_1$ such that their first fundamental quadratic form changes signature. Part of such a surface is space-like and part is time-like. We obtain complete information about the structure of the set of points where the surface changes type and prove the related existence and uniqueness theorems.


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English version:
Izvestiya: Mathematics, 2003, 67:2, 209–224

Bibliographic databases:

UDC: 517.957+514.752
MSC: 35F20, 35M05, 53A10, 53C21, 53C50, 65P05
Received: 13.03.2002

Citation: V. A. Klyachin, “Zero mean curvature surfaces of mixed type in Minkowski space”, Izv. RAN. Ser. Mat., 67:2 (2003), 5–20; Izv. Math., 67:2 (2003), 209–224

Citation in format AMSBIB
\by V.~A.~Klyachin
\paper Zero mean curvature surfaces of mixed type in Minkowski space
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 2
\pages 5--20
\jour Izv. Math.
\yr 2003
\vol 67
\issue 2
\pages 209--224

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    This publication is cited in the following articles:
    1. Akamine S., Honda A., Umehara M., Yamada K., “Bernstein-Type Theorem For Zero Mean Curvature Hypersurfaces Without Time-Like Points in Lorentz-Minkowski Space”, Bull. Braz. Math. Soc.  crossref  isi
    2. S. Fujimori, Y.W. Kim, S.-E. Koh, W. Rossman, H. Shin, H. Takahashi, M. Umehara, K. Yamada, S.-D. Yang, “Zero mean curvature surfaces in containing a light-like line”, Comptes Rendus Mathematique, 350:21-22 (2012), 975  crossref  mathscinet  zmath  isi  scopus
    3. Fujimori Sh., Rossman W., Umehara M., Yamada K., Yang S.-D., “Embedded Triply Periodic Zero Mean Curvature Surfaces of Mixed Type in Lorentz-Minkowski 3-Space”, Mich. Math. J., 63:1 (2014), 189–207  crossref  mathscinet  isi  scopus
    4. Fujimori S., Kim Y.W., Koh S.-E., Rossman W., Shin H., Umehara M., Yamada K., Yang S.-D., “Zero Mean Curvature Surfaces in Lorentz-Minkowski 3-Space Which Change Type Across a Light-Like Line”, Osaka J. Math., 52:1 (2015), 285–297  mathscinet  zmath  isi
    5. Branding V., Rossman W., “Magnetic geodesics on surfaces with singularities”, Pac. J. Math. Ind., 9 (2017)  crossref  mathscinet  zmath  isi
    6. Akamine Sh., “Causal Characters of Zero Mean Curvature Surfaces of Riemann Type in the Lorentz-Minkowski 3-Space”, Kyushu J. Math., 71:2 (2017), 211–249  crossref  mathscinet  zmath  isi  scopus
    7. Honda A., Koiso M., Kokubu M., Umehara M., Yamada K., “Mixed Type Surfaces With Bounded Mean Curvature in 3-Dimensional Space-Times”, Differ. Geom. Appl., 52 (2017), 64–77  crossref  mathscinet  zmath  isi  scopus
    8. Gao R., Wang F., Zhang X., Wang Yu., “Extremal Surface With the Light-Like Line in Minkowski Space R1+(1+1)”, Bound. Value Probl., 2017, 58  crossref  mathscinet  isi  scopus
    9. Fujimori Sh., Kawakami Yu., Kokubu M., Rossman W., Umehara M., Yamada K., “Analytic Extension of Jorge-Meeks Type Maximal Surfaces in Lorentz-Minkowski 3-Space”, Osaka J. Math., 54:2 (2017), 249–272  mathscinet  zmath  isi
    10. Umehara M., Yamada K., “Surfaces With Light-Like Points in Lorentz-Minkowski 3-Space With Applications”, Lorentzian Geometry and Related Topics, Geloma 2016, Springer Proceedings in Mathematics & Statistics, 211, eds. CanadasPinedo M., Flores J., Palomo F., Springer, 2017, 253–273  crossref  mathscinet  zmath  isi  scopus
    11. Honda A., Koiso M., Saji K., “Fold Singularities on Spacelike Cmc Surfaces in Lorentz-Minkowski Space”, Hokkaido Math. J., 47:2 (2018), 245–267  crossref  mathscinet  zmath  isi
    12. Stem A., Xu Ch., “Signature Change in Matrix Model Solutions”, Phys. Rev. D, 98:8 (2018), 086015  crossref  isi  scopus
    13. Akamine Sh., Singh R.K., “Wick Rotations of Solutions to the Minimal Surface Equation, the Zero Mean Curvature Equation and the Born-Infeld Equation”, Proc. Indian Acad. Sci.-Math. Sci., 129:3 (2019), UNSP 35  crossref  mathscinet  isi  scopus
    14. Umehara M., Yamada K., “Hypersurfaces With Light-Like Points in a Lorentzian Manifold”, J. Geom. Anal., 29:4 (2019), 3405–3437  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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