Abstract
We prove existence, uniqueness, and regularity for Dirichlet solutions of the stationary and axisymmetric Einstein equations in vacuum and in rigidly rotating ideal fluid matter for data (on a ball) whose absolute values are in a characteristic way limited by the ``diameter'' of the ball. These results have important consequences for the existence of exterior vacuum and interior matter solutions for rotating stars. The mathematical procedures and results have remarkable connections with a numerical solution technique for rotating stars.
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