arXiv:2208.10288 Abstract | arXiv Analytics

arXiv:2208.10288 [math.CA]Abstract References Reviews Resources

Subsets of rectifiable curves in Banach spaces II: universal estimates for almost flat arcs

Published 2022-08-22Version 1

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.

Comments: 50 pages, 8 figures; for part I, see arXiv:2002.11878

Categories: math.CA, math.FA, math.MG

Subjects: 28A75, 26A16, 46B20, 60G46

Keywords: banach space, rectifiable curve, universal estimates, flat arcs, straight line segments

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