自引力流体平衡形状的几何方法
A geometric approach to the equilibrium shapes of self-gravitating fluids
摘要：
黎曼流形中自引力流体可能的平衡形状的分类是数学物理中的一个经典问题。本文证明了平衡形是等参子流形。还得到了平衡形的一些几何性质，特别是与等周问题和流形的等距群的关系。这项工作遵循作者提出的新的几何方法（见math-ph/0305038）
英文摘要：
The classification of the possible 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 the equilibrium shapes are also obtained, specifically the relationship with the isoperimetric problem and the group of isometries of the manifold. This work follows the new geometric approach to the problem developed by the author (see math-ph/0305038)
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