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We show that the ground state interface geometry of binary condensates in thephase separated regime undergoes a smooth transition from planar to ellipsoidalto cylindrical geometry. This occurs for condensates with repulsiveinteractions as the trapping potential is changed from prolate to oblate. Thecorrect ground state geometry emerges when the interface energy is included inthe energy minimization. Where as energy minimization based on Thomas-Fermiapproximation gives incorrect geometry.

Ground State Geometry of Binary Condensates in Axisymmetric Traps