Annals of Global Analysis and Geometry

, Volume 13, Issue 1, pp 23–30 | Cite as

Some remarks on embedded hypersurfaces in hyperbolic space of constant curvature and spherical boundary

  • Barbara Nelli
  • Harold Rosenberg


We consider embedded hypersurfacesM in hyperbolic space with compact boundaryC and somerth mean curvature functionHr a positive constant. We investigate when symmetries ofC are symmetries ofM. We prove that if 0≤Hr≤1 andC is a sphere thenM is a part of an equidistant sphere. Forr=1 (H1 is the mean curvature) we obtain results whenC is convex.

Key words

Symmetries of hypersurfaces of constant curvature Alexandrov reflection flux formula 

MSC 1991

53A10 53C42 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Barbara Nelli
    • 1
  • Harold Rosenberg
    • 2
  1. 1.Dipartimento di MatematicaPisaItaly
  2. 2.Département de MathématiquesUniversité de Paris VIIParisFrance

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