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The structure of singly-periodic minimal surfaces

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References

  1. Callahan, M., Hoffman, D., Meeks III, W.H.: Embedded minimal surface with an infinite number of ends. Invent. Math.96, 459–505 (1989)

    Google Scholar 

  2. Choi, T., Meeks III, W.H., White, B.: A rigidity theorem for properly embedded minimal surfaces in ℝ3. J. Differ. Geom.

  3. Fischer-Colbrie, D.: On complete minimal surfaces with finite Morse index in 3-manifolds. Invent. Math.82, 121–132 (1985)

    Google Scholar 

  4. Freedman, M., Hass, J., Scott, P.: Closed geodesics on surfaces. Bull. Lond. Math. Soc.14, 385–391 (1982)

    Google Scholar 

  5. Hadamard, J.-J.: Les surfaces à courbures opposées et leurs lignes géodésiques. J. Math. Pures Appl.4, 27–73 (1898)

    Google Scholar 

  6. Hardt, R., Simon, L.: Boundary regularity and embedded minimal solutions for the oriented Plateau problem. Ann. Math.110, 439–486 (1979)

    Google Scholar 

  7. Hoffman, D., Meeks III, W.H.: The asymptotic behavior of properly embedded minimal surfaces of finite topology. J. Am. Math. Soc.2, No. 4, 667–681 (1989)

    Google Scholar 

  8. Hoffman, D., Meeks III, W.H.: The strong halfspace theorem for minimal surfaces. Invent. Math. (to appear)

  9. Hoffman, D., Meeks III, W.H.: A variational approach to the existence of complete embedded minimal surfaces. Duke J. Math.57, 877–894 (1988)

    Google Scholar 

  10. Huber, A.: On subharmonic functions and differential geometry in the large. Comment. Math. Helv.32, 181–206 (1957)

    Google Scholar 

  11. Karcher, H.: Embedded minimal surfaces derived from Scherk's examples. Manuscr. Math.62, 83–114 (1988)

    Google Scholar 

  12. Karcher, H., Pitts, J.: (personal communications)

  13. Meeks III, W.H., Rosenberg, H.: The geometry of periodic minimal surfaces (Preprint)

  14. Meeks III, W.H., Rosenberg, H.: The global theory of doubly periodic minimal surfaces. Invent. Math.97, 351–379 (1989)

    Google Scholar 

  15. Meeks III, W.H., Rosenberg, H.: The maximum principle at infinite for minimal surfaces in flat three-manifolds. Comm. Math. Helv. (to appear)

  16. Meeks III, W.H., Yau, S.T.: The topological uniqueness theorem of complete minimal surfaces of finite topological type (Preprint)

  17. Meeks III, W.H.: Yau, S.T.: The existence of embedded minimal surfaces and the problem of uniqueness. Math. Z.179, 151–168 (1982)

    Google Scholar 

  18. Morse, M.: Collected Papers. World Scientific, Singapore, 1987

    Google Scholar 

  19. Osserman, R.: Minimal surfaces in the large. Comment. Math. Helv.35, 65–76 (1961)

    Google Scholar 

  20. Osserman, R.: Global properties of minimal surfaces inE 3 andE n. Ann. Math.80, 340–364 (1964)

    Google Scholar 

  21. Schoen, R.: Uniqueness, symmetry, and embeddedness of minimal surfaces. J. Differ. Geom.18, 791–809 (1983)

    Google Scholar 

  22. Simon, L.: Lectures on geometric measure theory. In: Proceedings of the Center for Mathematical Analysis, vol. 3, Canberra, Australia, 1983. Australian National University

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The research described in this paper was supported by research grant DE-FG02-86ER250125 of the Applied Mathematical Science subprogram of Office of Energy Research, U.S. Department of Energy, and National Science Foundation grants DMS-8611574 and DMS-8802858

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Callahan, M., Hoffman, D. & Meeks, W.H. The structure of singly-periodic minimal surfaces. Invent Math 99, 455–481 (1990). https://doi.org/10.1007/BF01234428

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