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Function theory and index theory for minimal surfaces of genus 1; Part I: Fredholm bundles of holomorphic functions on punched tori

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References

  1. R.Böhme, A Plateau problem with many solutions. In: LNM838 (1981).

  2. R. Böhme andA. J. Tromba, The index theorem for classical minimal surfaces. Ann. of Math. (2)113, 447–499 (1981).

    Google Scholar 

  3. W. Koppelmann, The Riemann-Hilbert problem for finite Riemann surfaces. Comm. Pure Appl. Math.12, 13–35 (1959).

    Google Scholar 

  4. J. C. C.Nitsche, Vorlesung über Minimalflächen. Berlin-Heidelberg-New York 1975.

  5. T.Radó, On the problem of Plateau, subharmonic functions. Berlin-Heidelberg-New York 1971.

  6. K. Schüffler, Stabilität mehrfach zusammenhängender Minimalflächen. Manuscripta Math.30, 163–197 (1979).

    Google Scholar 

  7. K. Schüffler, Isoliertheit und Stabilität von Flächen konstanter mittlerer Krümmung. Manuscripta Math.40, 1–15 (1982).

    Google Scholar 

  8. K. Schüffler, Eine globalanalytische Betrachtung des Douglasschen Problems. Manuscripta Math.48, 189–226 (1984).

    Google Scholar 

  9. K. Schüffler undF. Tomi, Eine Indexsatz für Flächen konstanter mittlerer Krümmung. Math. Z.182, 245–257 (1983).

    Google Scholar 

  10. K. Schüffler, Zur Fredholmtheorie des Riemann-Hilbert Operators. Arch. Math.47, 359–366 (1986).

    Google Scholar 

  11. M. Söllner, Plateaus problem for surfaces of constant mean curvature from a global point of view. Manuscripta Math.43, 191–217 (1983).

    Google Scholar 

  12. K. Strebel, Ein Klassifizierungsproblem für Riemannsche Flächen vom Geschlecht 1. Arch. Math.48, 77–81 (1987).

    Google Scholar 

  13. U.Thiel, Der Indexsatz für mehrfach zusammenhängende Minimalflächen. Dissertation, Heidelberg 1983.

  14. F. Tomi andA. J. Tromba, On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy. J. Reine Angew. Math.316, 31–43 (1980).

    Google Scholar 

  15. A. J.Tromba, On the number of simply connected minimal surfaces spanning a curve. Mem. Amer. Math. Soc.194 (1977).

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Schüffler, K. Function theory and index theory for minimal surfaces of genus 1; Part I: Fredholm bundles of holomorphic functions on punched tori. Arch. Math 48, 250–266 (1987). https://doi.org/10.1007/BF01195359

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