Tangential tensor fields on deformable surfaces—how to derive consistent L2-gradient flows

Abstract

Abstract We consider gradient flows of surface energies that 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–Helfrich energy.