A Geometric Approach to the Classification of the Equilibrium Shapes of Self-Gravitating Fluids



The classification of the equilibrium shapes that a self-gravitating fluid can take in a Riemannian manifold is a classical problem in Mathematical Physics. In this paper it is proved that the equilibrium shapes are isoparametric submanifolds. Some geometric properties of them are also obtained, e.g. classification and existence for some Riemannian spaces and relationship with the isoperimetric problem and the group of isometries of the manifold. Our approach to the problem is geometrical and allows to study the equilibrium shapes on general Riemannian spaces.


Manifold Riemannian Manifold Equilibrium Shape Equilibrium Partition Round Sphere 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Departamento de Física Teórica IIUniversidad ComplutenseMadridSpain

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