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Möbius Geometry of Surfaces of Constant Mean Curvature 1 in Hyperbolic Space

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Abstract

An overview of the various transformations of isothermic surfaces and their interrelations is given using aquaternionic formalism. Applications to the theory of cmc-1 surfaces inhyperbolic space are given and relations between the two theories are discussed. Within this context, we give Möbius geometric characterizations for cmc-1 surfaces in hyperbolic space and theirminimal cousins.

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Authors and Affiliations

  1. Department of Mathematics, Technical University Berlin, Strasse des 17. Juni 135, D-10623, Berlin, Germany

    U. Hertrich-Jeromin

  2. Department of Mathematics, Università degli Studi di l'Aquila, I-67010, L'Aquila, Italy

    E. Musso

  3. Department of Mathematics, Università degli Studi di Roma `La Sapienza', I-00185, Rome, Italy

    L. Nicolodi

Authors
  1. U. Hertrich-Jeromin
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  2. E. Musso
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  3. L. Nicolodi
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Hertrich-Jeromin, U., Musso, E. & Nicolodi, L. Möbius Geometry of Surfaces of Constant Mean Curvature 1 in Hyperbolic Space. Annals of Global Analysis and Geometry 19, 185–205 (2001). https://doi.org/10.1023/A:1010738712475

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