Minimal Surfaces in Euclidean 3-Space and Their Mean Curvature 1 Cousins in Hyperbolic 3-Space

Shoichi Fujimori

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We show that the Hopf differentials of a pair of isometric cousin surfaces, a minimal surface in euclidean 3-space and a constant mean curvature (CMC) one surface in the 3-dimensional hyperbolic space, with properly embedded annular ends, extend holomorphically to each end. Using this result, we derive conditions for when the pair must be a plane and a horosphere.

Original languageEnglish
Pages (from-to)271-278
Number of pages8
JournalAnais da Academia Brasileira de Ciencias
Volume75
Issue number3
Publication statusPublished - Sep 2003
Externally publishedYes

Fingerprint

Minimal surface
Mean Curvature
Euclidean
Horosphere
Constant Mean Curvature
Hyperbolic Space
Isometric

Keywords

  • CMC 1 cousins
  • Hyperbolic space
  • Minimal surfaces

ASJC Scopus subject areas

  • General

Cite this

Minimal Surfaces in Euclidean 3-Space and Their Mean Curvature 1 Cousins in Hyperbolic 3-Space. / Fujimori, Shoichi.

In: Anais da Academia Brasileira de Ciencias, Vol. 75, No. 3, 09.2003, p. 271-278.

Research output: Contribution to journalArticle

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