Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent L²-Gradient Flows

2022/09/27 by Ingo Nitschke, Nitschke, Ingo, Souhayl Sadik +3 · 1 citation
Physics and Astronomy · #53A05 #53A45 #70G75 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.2209.13272

openalex publication_date 2022/09/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

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.

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