Subsets of rectifiable curves in Banach spaces II: Universal estimates for almost flat arcs
Copyright policy )Subsets of rectifiable curves in Banach spaces II: Universal estimates for almost flat arcs
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.
50 pages, 8 figures; for part I, see arXiv:2002.11878
- University of Connecticut United States
- National Taiwan Normal University Taiwan
Length, area, volume, other geometric measure theory, Lipschitz (Hölder) classes, Metric Geometry (math.MG), Functional Analysis (math.FA), Mathematics - Functional Analysis, Geometry and structure of normed linear spaces, Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, Martingales and classical analysis, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Primary 28A75, Secondary 26A16, 46B20, 60G46
Length, area, volume, other geometric measure theory, Lipschitz (Hölder) classes, Metric Geometry (math.MG), Functional Analysis (math.FA), Mathematics - Functional Analysis, Geometry and structure of normed linear spaces, Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, Martingales and classical analysis, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Primary 28A75, Secondary 26A16, 46B20, 60G46
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