Ground State Geometry of Binary Condensates in Axisymmetric Traps

We show that the ground state interface geometry of binary condensates in the phase separated regime undergoes a smooth transition from planar to ellipsoidal to cylindrical geometry. This occurs for condensates with repulsive interactions as the trapping potential is changed from prolate to oblate. The correct ground state geometry emerges when the interface energy is included in the energy minimization. Where as energy minimization based on Thomas-Fermi approximation gives incorrect geometry.