For zoom and focus applications in the UV and IR spectral range mirrors with actively deformable surfaces are promising for reflective adaptive optics as an alternative to refractive optics. To realise an adjustable focus length interval from infinity to the centimetre range the needed surface deformation can be described by a hemisphere. For shorter focus lengths and optical on-axis applications the parabolic shape has to be used. The actuation principle of a quasistatic micromirror with actively deformable surface can be realised using electrostatic, thermo-mechanic, piezoelectric or electromagnetic effects. This paper compares electrostatic, thermo-mechanic and piezoelectric actuation methods for deformable micromirrors. Thereby models of curved thin plates and estimations on power consumption for low frequency or quasistatic operation are discussed. Due to the low power consumption and the low driving voltage, the piezoelectric effect is determined as most promising driving principle for devices used in mobile applications.