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Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent $L^2$-Gradient Flows

Research output: Working paper/Preprint Preprint


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 to chose a notion of 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 energy.
Original languageEnglish
Publication statusPublished - 27 Sep 2022

Bibliographical note

31 pages, 4 figures, 2 videos

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