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On the regularity of minimal surfaces with free boundaries in Riemannian manifolds

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Abstract

We show c1,α-regularity of minimal surfaces in Riemannian manifolds with a free boundary on C2-hypersurfaces with bounded second fundamental form and a uniform neighborhood on which the nearest point projection is uniquely defined and differentiable. The decisive step is the proof of continuity at the free boundary.

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References

  1. Buser, P. and H. Karcher, Gromov's almost flat manifolds, Astérisque 81 (1981)

  2. Dziuk, G., Über die Stetigkeit teilweise freier Minimalflächen, man. math. 36 (1981), 241–251

    Google Scholar 

  3. Dziuk, G., C2-regularity for partially free minimal surfaces, MZ 189 (1985), 71–79

    Google Scholar 

  4. Grüter, M., Regularity of weak H-surfaces, Journ. reine angew. Math. 329 (1981), 1–15

    Google Scholar 

  5. Grüter, M., Hildebrandt, S. and J.C.C. Nitsche, On the boundary behaviour of minimal surfaces with a free boundary which are not minima of the area, man. math. 35 (1981), 387–410

    Google Scholar 

  6. Grüter, M. and J. Jost, Allard type regularity results for minimal surfaces with free boundaries, Ann. Sc. Norm. Sup. Pisa, to appear

  7. Jost, J., Harmonic mappings between Riemannian manifolds, Canberra, 1984

  8. Jost, J. and H. Karcher, Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen, man. math. 40 (1982), 27–77

    Google Scholar 

  9. Küster, A., An optimal estimate of the free boundary of a minimal surface, Journ. reine angew. Math., to appear

  10. Ye, R., Randregularität von Minimalflächen, Diplomarbeit, Bonn 1984

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut der Ruhr-Universität Bochum, D-4630, Bochum, Germany

    Jürgen Jost

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  1. Jürgen Jost
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partially supported by SFB 72 (Deutsche Forschungsgemeinschaft)

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Jost, J. On the regularity of minimal surfaces with free boundaries in Riemannian manifolds. Manuscripta Math 56, 279–291 (1986). https://doi.org/10.1007/BF01180769

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  • DOI: https://doi.org/10.1007/BF01180769

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