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arXiv · 2012.10691

Rectifiable curves in proximally smooth sets

Grigory Ivanov·Mariana Lopushanski
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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.

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Grigory Ivanov, Mariana Lopushanski. 2020-12-19. Rectifiable curves in proximally smooth sets. https://arxiv.org/abs/2012.10691

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