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Vortex states of weakly-interacting Bose-Einstein condensates confined inthree-dimensional rotating harmonic traps are investigated numerically at zerotemperature. The ground state in the rotating frame is obtained by propagatingthe Gross-Pitaevskii equation for the condensate in imaginary time. The totalenergies between states with and without a vortex are compared, yieldingcritical rotation frequencies that depend on the anisotropy of the trap and thenumber of atoms. Vortices displaced from the center of nonrotating traps arefound to have long lifetimes for sufficiently large numbers of atoms. Therelationship between vortex stability and bound core states is explored.Comment: 5 pages, 2 embedded figures, revtex. To appear in Phys. Rev. Let

Vortex Stability of Interacting Bose-Einstein Condensates Confined in Anisotropic Harmonic Traps