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, Volume 59, Issue 3, pp 277–294 | Cite as

New examples of imbedded spherical soap bubbles inS N (1)

  • Ivan Sterling


A. D. Alexandrov proved that the only imbedded soap bubbles in euclidean or hyperbolicn-space are round spheres. This also holds for ann-dimensional hemisphere. In this paper we give many new examples of differentiable (n−1)-spheres imbedded as soap bubbles in sphericaln-space. Thus we show Alexandrov's theorem is false for sphericaln-space even under the added assumption that the soap bubbles are differentiable (n−1)-spheres.


Number Theory Algebraic Geometry Topological Group Round Sphere Soap Bubble 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Ivan Sterling
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaSanta CruzUSA
  2. 2.Fachbereich 3-MathematikTU BerlinBerlin 12

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