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Multidimensional parametrized variational problems on riemannian manifolds

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References

  1. L. Young. Lectures on the calculus of variations and optimal control theory. W.B.Saunders company, Philadelphia-London-Toronto, 1969.

    MATH  Google Scholar 

  2. G.de Rham. Variétés différentiables. Formes courantes, formes harmoniques.-Actualités Sc.Indust., no. 1222, Paris, 1955.

    Google Scholar 

  3. A.T. Fomenko. Multidimensional Plateau problem on Riemannian manifolds. On the problem of the algorithmical recognizability of the standard three-dimensional sphere.-Proc.Internat.Congr.Math. (Vancouver, 1974), vol.2 (1975), 515–523.

    MathSciNet  MATH  Google Scholar 

  4. A.T. Fomenko. The multidimensional Plateau problem in Riemannian manifolds.-Mat.Sb., 1972, 89 (131), No. 3, 475–520 (in Russian); English transl.in Math.USSR sb. 18 (1972)).

    MathSciNet  Google Scholar 

  5. A.T. Fomenko. Multidimensional Plateau problems on Riemannian manifolds, and extraordinary homology and cohomology theories, I.-Trudy Sem.Vektor.Tenzor.Anal., v.17 (1974), 3–176 (in Russian).

    MathSciNet  MATH  Google Scholar 

  6. Dao Chong Thi (Đaò Trong Thi). Multivarifolds and classical multidimensional Plateau problems.-Izv.Akad.Nauk SSSR, 1980, v.44, No 5, 1031–1065 (in Russian; English transl.in Math.USSR Izv., 17 (1981)).

    MathSciNet  Google Scholar 

  7. Dao Chong Thi (Đào Trong Thi). The spaces of parametrizations and parametrized multivarifolds.-Trudy Sem.Vector.Tenzor.Anal., 1985, v.22 (in Russian).

    Google Scholar 

  8. H. Federer. Geometric measure theory. Berlin,Springer, 1969.

    MATH  Google Scholar 

  9. H. Federer,W.H. Fleming. Normal and integral currents.-Ann.Math., 1960, 72, No.3, 458–520.

    Article  MathSciNet  MATH  Google Scholar 

  10. F.J. Almgren. Existence and regularity almost everywhere of solutions to elliptic variational problem among of varying topological type and singularity structure.-Ann.Math.,1968,87,No.2, 321–391.

    Article  MathSciNet  MATH  Google Scholar 

  11. F.J. Almgren. Plateau’s problem. An invitation to varifold geometry. New York, Benjamin, 1966.

    MATH  Google Scholar 

  12. T. Rado. On the problem of least area and the problem of Plateau.-Math.Z., 1930, v.32, 763–796.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Douglas. Solution of the problem of Plateau.-Trans.Amer.Math. Soc., 1931, v.33, 263–321.

    Article  MathSciNet  MATH  Google Scholar 

  14. R.Courant. Dirichlet’s principle, conformal mapping, and minimal surfaces. Interscience, 1950.

    Google Scholar 

  15. Ch.B. Morrey. Multiple integrals on the calculus of variations. Berlin, Springer, 1966.

    MATH  Google Scholar 

  16. E.R. Riefenberg. Solution of the Plateau problem for m-dimensional surfaces of varying topological type.-Acta Math., 1960, v.104, No.1, 1–92.

    Article  MathSciNet  Google Scholar 

  17. M. Golubitsky, V. Guillemin. Stable mappings and their singularities Springer-Verlag, New York, Heidelberg, Berlin, 1973.

    Book  MATH  Google Scholar 

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Yuriǐ G. Borisovich Yuriǐ E. Gliklikh A. M. Vershik

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© 1986 Springer-Verlag

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Thi, Đ.T. (1986). Multidimensional parametrized variational problems on riemannian manifolds. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications II. Lecture Notes in Mathematics, vol 1214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075958

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  • DOI: https://doi.org/10.1007/BFb0075958

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16821-8

  • Online ISBN: 978-3-540-47084-7

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