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Constant mean curvature surfaces constructed by fusing Wente tori

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References

  • [Ab1] U. Abresch: Constant mean curvature tori in terms of elliptic functions. J. Reine Angew. Math.374, 169–192 (1987)

    Google Scholar 

  • [Ab2] U. Abresch: Old and new periodic solutions of the sinh-Gordon equation. Seminar on new results in non-linear partial differential equations. Braunschweig: Vieweg (1987)

    Google Scholar 

  • [A] A. D. Alexandrov: Uniqueness theorems for surfaces in the largeI, Vestnik Leningrad Univ. Math.11, 5–17 (1956)

    Google Scholar 

  • [Bo] A. I. Bobenko: All constant mean curvature tori in ℝ3,\(\mathbb{S}^3 \), ℍ3 in terms of theta-functions. Math. Ann.290, 209–245 (1991)

    Google Scholar 

  • [B-dC] L. Barbosa, M. doCarmo: Stability of hypersurfaces with constant mean curvature. Math. Z.185, 339–353 (1984)

    Google Scholar 

  • [Ch] I. Chavel: Eigenvalues in Riemannian Geometry. London: Academic Press, 1984

    Google Scholar 

  • [C] S. S. Chern: Some new characterizations of the Euclidean sphere. Duke Math. J.12, 279–290 (1945)

    Google Scholar 

  • [D] D. Delaunay: Sur la surface de revolution dont la courbure moyenne est constante. J. Math. Pures Appl.6, 309–320 (1841)

    Google Scholar 

  • J. Dorfmeister, H. Wu: Constant mean curvature surfaces and loop groups (Preprint)

  • [E-K-T] N. Ercolani, H. Knorrer, E. Trubowitz: Hyperelliptic curves that generate constant mean curvature tori inR 3. The Verdier Memorial Conference in Integrable Systems: Actes du colloque international de luminy (1991), ed. by Olivier Babelon, Pierre Cartier and Yvette Kosmann-Schwarzbach, Basel: Birkhäuser

    Google Scholar 

  • [G-T] D. Gilbarg, N. S. Trudinger: Elliptic partial differential equations of second order. 2nd Edition, Berlin Heidelberg New York: Springer, 1983

    Google Scholar 

  • H. Hopf: Lectures on Differential Geometry in the Large. Notes by John Gray, Stanford University

  • [HS] Wu-Yi Hsiang: Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces, I. J. Differ. Geom.17, 337–356 (1982)

    Google Scholar 

  • [J] J. H. Jellet: Sur la surface dont la coubure moyenne est constante. J. Math. Pures Appl.18, 163–167 (1853)

    Google Scholar 

  • [K1] N. Kapouleas: Constant mean curvature surfaces in Euclidean three-space. Bull. AMS17, 318–320 (1987)

    Google Scholar 

  • [K2] N. Kapouleas: Complete constant mean curvature surfaces in Euclidean three-space. Ann. Math. (2)131, 239–330 (1990)

    Google Scholar 

  • [K3] N. Kapouleas: Compact constant mean curvature surfaces in Euclidean three-space. J. Differ. Geom.33, 683–715 (1991)

    Google Scholar 

  • [K4] N. Kapouleas: Constant mean curvature surfaces constructed by fusing Wente tori. Proc. Nat. Acad. Sci. USA89, 5695–5698 (1992)

    Google Scholar 

  • [K-K-S] N. Korevaar, R. Kusner, B. Solomon: The structure of complete embedded surfaces with constant mean curvature. J. Diff. Geom.30, 465–503 (1989)

    Google Scholar 

  • [P-S] U. Pinkall, I. Sterling: On the classification of constant mean curvature tori. Ann. Math.130, 407–451 (1989)

    Google Scholar 

  • [Tr] F. Tricomi, M. Krafft Elliptische Functionen. Leipzig: Akad, Verl. Ges. Geest. u. Portig, 1948

    Google Scholar 

  • M. Timmreck, U. Pinkall, D. Ferus: Constant mean curvature planes with inner rotational symmetry in Euclidean 3-space (Preprint)

  • [Wa] R. Walter: Explicit examples to the H-Problem of Heinz Hopf. Geom. Dedicata23, 187–213 (1987)

    Google Scholar 

  • [W1] H. C. Wente: Counterexample to a conjecture of H. Hopf. Pac. J. Math.121, 193–243 (1986)

    Google Scholar 

  • [W2] H. C. Wente: Twisted tori of constant mean curvature inR 3, Seminar on new results in non-linear partial differential equations. Braunschweig: Vieweg 1987

    Google Scholar 

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Oblatum 12-IV-1993 & 23-XI-1993

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Kapouleas, N. Constant mean curvature surfaces constructed by fusing Wente tori. Invent Math 119, 443–518 (1995). https://doi.org/10.1007/BF01245190

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