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Relative calibrations and the problem of stability of minimal surfaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1453)

Keywords

  • Minimal Surface
  • Lagrangian Submanifolds
  • Hermitian Manifold
  • Relative Calibration
  • Normal Vector Field

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References

  1. Đào Trong Thi. Minimal real currents on compact Riemannian manifolds. Izv. Akad. Nauk. SSSR, Ser. Math.-1977, t.41, N 4, p.853–867.

    MathSciNet  MATH  Google Scholar 

  2. Đào Trong Thi, Fomenko A.T. Minimal surfaces and the Plateau's problem, Moscow, Nauka, 1987.

    MATH  Google Scholar 

  3. Dynkin E.B. Topological characteristics of homomorphisms of Lie compact groups, Mat. sbornik.-1954, 35, N 1, p.129–173.

    MathSciNet  Google Scholar 

  4. Kobayshi S., Nomizu K. Foundation of differential geometry, Intersci. Publishers, New York-London, 1969.

    Google Scholar 

  5. Le Hong Van. Absolutely minimal surfaces and gauges in adjoint orbits of classical Lie groups, Dokl. Akad. Nauk, 1988,-298, N 6, p.1308–1311.

    Google Scholar 

  6. Le Hong Van, Fomenko A.T. Criterion for minimality of Lagrangian submanifolds in Kähler manifolds, Math. Zametky, 1987, t.42, N 4, p.559–571.

    MATH  Google Scholar 

  7. Brother J. Stability of minimal orbits. Trans. Amer. Math. Soc., 1986, t.294, N 2, p.537–552.

    CrossRef  MathSciNet  Google Scholar 

  8. Bryant R.L. Minimal Lagrangian submanifolds of Kahler-Einstein manifolds. Lect. Notes in Math.-1987, 1255, p.1–12.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Federer H. Geometric measure theory. Berlin: Springer, 1969.

    MATH  Google Scholar 

  10. Harvey R., Lawson H.B. Calibrated geometries. Acta Math. 1982, p.47–157.

    Google Scholar 

  11. Morgan F. The exterior algebra Λ Rn and area minimization. Linear Alg. & App., 1985,-66, p.1–38.

    CrossRef  Google Scholar 

  12. Simons J. Minimal varieties in Riemannian manifolds. Ann. Math.-1968, p.62–105.

    Google Scholar 

  13. Le Hong Van. Minimal Lagrangian surfaces in almost Hermitian spaces. Mat. Sbornik, 1989 (in Russian).

    Google Scholar 

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© 1990 Springer-Verlag

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Van Hong, L. (1990). Relative calibrations and the problem of stability of minimal surfaces. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis - Studies and Applications IV. Lecture Notes in Mathematics, vol 1453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085959

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  • DOI: https://doi.org/10.1007/BFb0085959

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  • Print ISBN: 978-3-540-53407-5

  • Online ISBN: 978-3-540-46861-5

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