论文标题
可变形表面上的切向张量字段 - 如何得出一致的$ l^2 $ - 级别流量
Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent $L^2$-Gradient Flows
论文作者
论文摘要
我们考虑通过参数化和切向张量场取决于表面的表面能的梯度流。流量可以通过同时发展参数化和张量场来耗散。这需要选择独立的符号。我们介绍了表面独立性的不同量表，并显示出它们对进化的后果。为了确保能量减少，必须始终选择表面独立性和时间导数的量表。我们证明了表面弗兰克 - 俄亥俄 - 希尔夫里夫能的结果。
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.
