  We consider gradient flows of surface energies which depend on the surface by
a parameterization and on a tangential tensor field. The flow allows for
dissipation by evolving the parameterization and the tensor field
simultaneously. This requires the choice of a notation for independence. We
introduce different gauges of surface independence and show their consequences
for the evolution. In order to guarantee a decrease in energy, the gauge of
surface independence and the time derivative have to be chosen consistently. We
demonstrate the results for a surface Frank-Oseen-Hilfrich energy.
