  We study the Kelvin mode excitations on a vortex line in a three-dimensional
trapped Bose-Einstein condensate at finite temperature. Our stochastic
Gross-Pitaevskii simulations show that the activation of these modes can be
suppressed by tightening the confinement along the direction of the vortex
line, leading to a strong suppression in the vortex decay rate as the system
enters a regime of two-dimensional vortex dynamics. As the system approaches
the condensation transition temperature we find that the vortex decay rate is
strongly sensitive to dimensionality and temperature, observing a large
enhancement for quasi-two-dimensional traps. Three-dimensional simulations of
the recent vortex dipole decay experiment of Neely et al. [Phys. Rev. Lett.
104, 160401 (2010)] confirm two-dimensional vortex dynamics, and predict a
dipole lifetime consistent with experimental observations and suppression of
Kelvon-induced vortex decay in highly oblate condensates.
