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Regularity and finiteness of solutions to the free boundary problem for minimal surfaces

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Bibliography

  1. Alt, H.W.: Verzweigungspunkte vonH-Flächen. II. Math. Ann.201, 33–55 (1973)

    Google Scholar 

  2. Courant, R.: Dirichlet's principle, conformal mapping, and minimal surfaces. New York: Interscience 1950

    Google Scholar 

  3. Dziuk, G.: Über die Stetigkeit teilweise freier Minimalflächen. Manuscr. Math.36, 241–251 (1981)

    Google Scholar 

  4. Grüter, M., Hildebrandt, S., Nitsche, J.C.C.: On the boundary behavior of minimal surfaces with a free boundary which are not minima of the area. Manuscr. Math.35, 387–410 (1981)

    Google Scholar 

  5. Gulliver, R.D.: Regularity of minimizing surfaces of prescribed mean curvature. Ann. of Math.97, 275–305 (1973)

    Google Scholar 

  6. Hildebrandt, S., Nitsche, J.C.C.: Geometric properties of minimal surfaces with free boundaries. Math. Z.184, 497–509 (1983)

    Google Scholar 

  7. Jäger, W.: Behavior of minimal surfaces with free boundaries. Commun. Pure Appl. Math.23, 803–818 (1970)

    Google Scholar 

  8. Lewy, H.: On minimal surfaces with free boundaries. Commun. Pure Appl. Math.4, 1–13 (1951)

    Google Scholar 

  9. Meeks, W.H., Yau, S.T.: Topology of three dimensional manifolds and the embedding problems in minimal surface theory. Ann. of Math.112, 441–484 (1980)

    Google Scholar 

  10. Ossermann, R.: A proof of the regularity everywhere of the classical solution to Plateau's problem. Ann. of Math.91, 550–569 (1970)

    Google Scholar 

  11. Tomi, F.: A finiteness result in the free boundary value problem for minimal surfaces. To appear

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Dedicated to E. Heinz on occasion of his sixtieth birthday

Supported by Deutsche Forschungsgemeinschaft, SFB 72

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Alt, H.W., Tomi, F. Regularity and finiteness of solutions to the free boundary problem for minimal surfaces. Math Z 189, 227–237 (1985). https://doi.org/10.1007/BF01175046

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