Rectifiable curves in proximally smooth sets
Functional Analysis
2020-12-22 v1 Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2012.10691,
title = {Rectifiable curves in proximally smooth sets},
author = {Grigory Ivanov and Mariana Lopushanski},
journal= {arXiv preprint arXiv:2012.10691},
year = {2020}
}