论文标题
近端平滑集中的可整流曲线
Rectifiable curves in proximally smooth sets
论文作者
论文摘要
我们提供了一种算法，该算法是在均匀凸出和均匀光滑的Banach空间中的两个足够接近点之间构造可重新构建曲线的算法。我们的算法返回一个相当短的曲线，在两个足够平滑集的两个足够接近点之间是迭代的，并使用了度量投影的一定修改。我们估计构造曲线的长度及其与段相同端点的段偏差。这些估计值与在希尔伯特空间中近端平滑的近端平滑设置中相吻合的因素是一个恒定的因素。
We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space. Our algorithm returns a reasonably short curve between two sufficiently close points of a proximally smooth set, is iterative and uses a certain modification of the metric projection. We estimate the length of a constructed curve and its deviation from the segment with the same endpoints. These estimates coincide up to a constant factor with those for the geodesics in a proximally smooth set in a Hilbert space.
