Subsets of rectifiable curves in Banach spaces II: universal estimates for almost flat arcs
Classical Analysis and ODEs
2022-08-23 v1 Functional Analysis
Metric Geometry
Abstract
We prove that in any Banach space the set of windows in which a rectifiable curve resembles two or more straight line segments is quantitatively small with constants that are independent of the curve, the dimension of the space, and the choice of norm. Together with Part I, this completes the proof of the necessary half of the Analyst's Traveling Salesman theorem with sharp exponent in uniformly convex spaces.
Keywords
Cite
@article{arxiv.2208.10288,
title = {Subsets of rectifiable curves in Banach spaces II: universal estimates for almost flat arcs},
author = {Matthew Badger and Sean McCurdy},
journal= {arXiv preprint arXiv:2208.10288},
year = {2022}
}
Comments
50 pages, 8 figures; for part I, see arXiv:2002.11878