Abstract
The equilibrium shape and the fission barrier are calculated for the entire range of angular momenta for which a rotating droplet held together by surface tension has a stable equilibrium. A liquid drop which is originally spherical takes the shape of an oblate spheroid as the angular momentum increases. At higher angular momenta, the shape becomes concave at the poles and a ring form is created. It is shown that the equilibrium ceases to be stable at or near the critical angular momentum at which this change of topology occurs.

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