Vortex gyrotropic mode in curved nanodots

•Vortex gyrotropic mode frequency depends on the nanodot curvature parameter.•The uniform out of plane magnetization is forming in the apex of the curved nanodots.•Vortex gyrotropic frequency is influenced strongly by the magnetization state of the nanodot apex.•The apex influence on the vortex oscillations can be diminished by the magnetic field.