Pseudogradient Flows of Geometric Energies
Pseudogradient Flows of Geometric Energies
复制标题
几何能量的伪梯度流
DOI：
10.1515/9783110571493-004
复制
发表时间：
2017
影响因子：
2.1
通讯作者：
Henrik Schumacher
中科院分区：
文献类型：
--
作者：
Henrik Schumacher
对于黎曼流形上的可微函数，梯度向量场及其诱导梯度流是定义良好且易于理解的概念.不幸的是，许多非二次的、无限维的优化问题不能在黎曼流形上以方便的方式表述.我们引入一类无限维的Banach流形，它允许我们定义广义梯度.此外，我们显示短期存在的诱导流和应用其离散化的数值最小化的各种几何能量的浸没曲线和曲面。
For differentiable functions on Riemannian manifolds, the gradient vector field and its inducedgradient flowarewell-definedandwell-understood concepts.Unfortunately, many nonquadratic, infinite-dimensional optimization problems cannot be formulated on Riemannianmanifolds in a convenient way.We introduce a category of infinite-dimensional Banachmanifolds that allows us to define a generalized gradient. Moreover, we show short-time existence of the induced flows and apply their discretizations to the numerical minimization of various geometric energies of immersed curves and surfaces.