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Harmonic maps between unbounded convex polyhedra in hyperbolic spaces

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References

  • [A] Akutagawa, K.: Harmonic diffeomorphisms of the hyperbolic plane. Trans. Am. Math. Soc. (to appear)

  • [ANT] Akutagawa, K., Nishikawa, S., Tachikawa, A.: Harmonic maps of unbounded convex polygons in the hyperbolic plane. In: Geometry and its Applications. Proceedings of the Workshop in honor of Morio Obata. pp. 17–19. Singapore: World Scientific 1993

    Google Scholar 

  • [CT] Choi, H.I., Treibergs, A.: Gauss map of spacelike constant mean curvature hypersurfaces of Minkowski space. J. Differ. Geom.32, 775–817 (1990)

    Google Scholar 

  • [EO] Eberlein, P., O'Neill, B.: Visibility manifolds. Pac. J. Math.46, 45–109 (1973)

    Google Scholar 

  • [GH] Giaquinta, M., Hildebrandt, S.: A priori estimates for harmonic mappings. J Reine Angew. Math.336, 124–164 (1982)

    Google Scholar 

  • [GT] Gilberg, D., Trudinger, N.S.: Partial Differential Equations of Second Order, second edition. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  • [HKW] Hildebrandt, S., Kaul, H., Widman, K.O.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math.138 1–16 (1977)

    Google Scholar 

  • [JaK] Jäger, J., Kaul, H.: Uniqueness and stability of harmonic maps and their Jacobi fields. Manuscr. Math.28, 269–291 (1979)

    Google Scholar 

  • [J1] Jost, J.: Harmonic maps between surfaces. (Lect. Notes Math., Vol. 1062) Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  • [J2] Jost, J.: Harmonic mappings between Riemannian manifolds. (Proc. Cent. Math. Anal., Vol. 4) Canberra: Australian National University Press 1984

    Google Scholar 

  • [JoK] Jost, J., Karcher, H.: Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen. Manuscr. Math.40, 27–77 (1982)

    Google Scholar 

  • [LT1] Li, P., Tam, L.-F.: The heat equation and harmonic maps of complete manifolds. Invent. Math.105, 1–46 (1991)

    Google Scholar 

  • [LT2] Li, P., Tam, L.-F.: Uniqueness and regularity of proper harmonic maps. Ann. Math.137, 167–201 (1993)

    Google Scholar 

  • [LT3] Li, P., Tam, L.-F.: Uniqueness and regularity of proper harmonic maps. II. Indiana Math. J. (to appear)

  • [M] Maskit, B.: Kleinian Groups. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  • [N] Nehari, Z.: Conformal mapping. New York: Dover 1975

    Google Scholar 

  • [SY] Schoen, R., Yau, S-T. On univalent harmonic maps between surfaces. Invent. Math.44, 265–278 (1978)

    Google Scholar 

  • [W] Wan, T.: Constant mean curvature surfaces, harmonic maps and universal Teichmüller space. J. Differ. Geom.35, 643–657 (1992)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shizuoka University, 422, Shizuoka, Japan

    Kazuo Akutagawa & Atsushi Tachikawa

  2. Mathematical Institute, Tohoku University, 980, Sendai, Japan

    Seiki Nishikawa

Authors
  1. Kazuo Akutagawa
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  2. Seiki Nishikawa
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  3. Atsushi Tachikawa
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Additional information

Dedicated to Professor Takeshi Kotake on his 60th birthday

Oblatum 20-I-1993 & 19-VII-1993

Researches of the first and the third authors were partially supported by the Grants-in-Aid for Scientific Research No. 04640220 and No. 04740026

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Akutagawa, K., Nishikawa, S. & Tachikawa, A. Harmonic maps between unbounded convex polyhedra in hyperbolic spaces. Invent Math 115, 391–404 (1994). https://doi.org/10.1007/BF01231765

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