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Classical area minimizing surfaces with real-analytic boundaries

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Acta Mathematica

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References

  • [Alm]Almgren, F. J., Jr.,Q-valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two. Preprint.

  • [Alt]Alt, H. W., Verzweigungspunkte vonH-Flächen, I.Math. Z., 127 (1972), 333–362; II.Math. Ann., 201 (1973), 33–55.

    Article  MATH  MathSciNet  Google Scholar 

  • [C]Chang, S., Two-dimensional area minimizing integral currents are classical minimal surfaces.J. Amer. Math. Soc., 1 (1988), 699–778.

    Article  MATH  MathSciNet  Google Scholar 

  • [F]Federer, H., Some theorems on integral currents.Trans. Amer. Math. Soc., 117 (1965), 43–67.

    Article  MATH  MathSciNet  Google Scholar 

  • [G1]Gulliver, R., Regularity of minimizing surfaces of prescribed mean curvature.Ann. of Math., (2), 97 (1973), 275–305.

    Article  MATH  MathSciNet  Google Scholar 

  • [G2]-—, Branched immersions of surfaces and reduction of topological type, II.Math. Ann., 230 (1977), 25–48.

    Article  MATH  MathSciNet  Google Scholar 

  • [G3]-—, A minimal surface with an atypical boundary branch point, inDifferential Geometry, pp. 211–228. Pitman Monographs Surveys Pure Appl. Math., 52. Longman Sci. Tech., Harlow, 1991.

    Google Scholar 

  • [GL]Gulliver, R. &Lesley, F., On the boundary branch points of minimizing surfaces.Arch. Rational Mech. Anal., 52 (1973), 20–25.

    Article  MathSciNet  Google Scholar 

  • [GOR]Gulliver, R., Osserman, R. &Royden, H., A theory of branched immersions of surfaces.Amer. J. Math., 95 (1973), 750–812.

    MathSciNet  Google Scholar 

  • [HH]Heinz, E. &Hildebrandt, S., Some remarks on minimal surfaces in Riemannian manifolds.Comm. Pure Appl. Math., 23 (1970), 371–377.

    MathSciNet  Google Scholar 

  • [HS]Hardt, R. &Simon, L., Boundary regularity and embedded solutions for the oriented Plateau problem.Ann. of Math. (2), 110 (1979), 439–486.

    Article  MathSciNet  Google Scholar 

  • [MW]Micallef, M. J. &White, B., The structure of branch points in minimal surfaces and in pseudoholomorphic curves.Ann. of Math. (2), 141 (1995), 35–85.

    Article  MathSciNet  Google Scholar 

  • [N]Nitsche, J. C. C.,Lectures on Minimal Surfaces, Vol. 1. Cambridge Univ. Press, Cambridge-New York, 1989.

    Google Scholar 

  • [O]Osserman, R., A proof of the regularity everywhere of the classical solution to Plateau's problem.Ann. of Math. (2), 91 (1970), 550–569.

    Article  MATH  MathSciNet  Google Scholar 

  • [W]White, B., Half of Enneper's surface minimizes area, inGeometric Analysis and the Calculus of Variations, pp. 361–367. Internat. Press, Cambridge, MA, 1996.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA, U.S.A.

    Brian White

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  1. Brian White
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The author was partially funded by NSF Grants DMS-9207704 and DMS-9504456

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White, B. Classical area minimizing surfaces with real-analytic boundaries. Acta Math. 179, 295–305 (1997). https://doi.org/10.1007/BF02392746

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  • DOI: https://doi.org/10.1007/BF02392746

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