Surfaces of Minimal Area Supported by a Given Body in ℝ3

  • G. Mancini
  • R. Musina
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)


Existence theory in the “Plateau problem” is mostly concerned with surfaces spanning some given boundary configuration ([A], [Cou], [HiN], [GJ], [S], to quote a few).


Riemannian Manifold Variational Inequality Minimal Surface Minimal Area Free Boundary Problem 
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    Brezis, H., Coron,J.M.: Large solutions for harmonic maps in two dimensions, Comm. Math. Phys. 92, 203 – 215 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
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    Courant, R.: Dirichlet principle, conformal mappings and minimal surfaces, Interscience, New York, 1950.Google Scholar
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    Hildebrandt, S.: On the regularity of solutions of two-imensional variational problems with obstructions, Comm. Pure Appl. Math. 25, 479-496 (1972)Google Scholar
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    Lions, P.L.: The concentration-Compactness principle in the Calculus of Variations: the limit case, Rev. Mat. Iberoamericana 1, 145-201 vol. 1 and 45 – 121 vol. 2 (1985)CrossRefGoogle Scholar
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    Musina R.: S2-type minimal surfaces enclosing many obstacles in R3, preprint. [MM] Mancini G., R. Musina: Surfaces of minimal area enclosing a given body in IR3 . Google Scholar
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    Micaleff M.J., J.D. Moore: Minimal two spheres and the topology of manifolds with positive curvature on totally isotropic two planes, Ann. of Math., 198-227(1988).Google Scholar
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • G. Mancini
    • 1
  • R. Musina
    • 2
  1. 1.Dipartimento di MatematicaUniversità di BolognaItaly
  2. 2.SISSATriesteItaly

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