Subsets of rectifiable curves in Banach spaces. I: Sharp exponents in traveling salesman theorems
From MaRDI portal
Publication:6113393
DOI10.1215/00192082-10592363arXiv2002.11878OpenAlexW4362685333WikidataQ123142237 ScholiaQ123142237MaRDI QIDQ6113393
Publication date: 9 August 2023
Published in: Illinois Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2002.11878
Numerical smoothing, curve fitting (65D10) Lipschitz (Hölder) classes (26A16) Geometry and structure of normed linear spaces (46B20) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80)
Related Items (3)
Subsets of rectifiable curves in Banach spaces. II: Universal estimates for almost flat arcs ⋮ A \(d\)-dimensional analyst's travelling salesman theorem for subsets of Hilbert space ⋮ Identifying 1-rectifiable measures in Carnot groups
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Weak parallelogram laws on Banach spaces and applications to prediction
- Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps
- On the structure of continua with finite length and Gołąb's semicontinuity theorem
- Multiscale analysis of 1-rectifiable measures. II: Characterizations
- Bilipschitz homogeneity and inner diameter distance
- Geometry and topology of intrinsic distances
- Quasicircles modulo bilipschitz maps
- The normalized duality mapping and two related characteristic properties of a uniformly convex Banach space
- On the uniform convexity of \(L^p\) and \(l^p\)
- Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
- Rectifiable sets and the traveling salesman problem
- Generalized rectifiability of measures and the identification problem
- Characterization of \(n\)-rectifiability in terms of Jones' square function. II
- Subsets of rectifiable curves in Hilbert space-the analyst's TSP
- Menger curvature and rectifiability in metric spaces
- Wiggly sets and limit sets
- Geometry of Banach spaces. Selected topics
- Harmonic measure, \(L^ 2\) estimates and the Schwarzian derivative
- Rectifiable sets in metric and Banach spaces
- An analyst's traveling salesman theorem for sets of dimension larger than one
- Painlevé's problem and the semiadditivity of analytic capacity.
- A bound for the modulus of continuity for metric projections in a uniformly convex and uniformly smooth Banach space
- Hölder parameterization of iterated function systems and a self-affine phenomenon
- The Besicovitch-Federer projection theorem is false in every infinite-dimensional Banach space
- A sharp necessary condition for rectifiable curves in metric spaces
- The restricted content and the \(d\)-dimensional Analyst's travelling salesman theorem for general sets
- Box-counting by Hölder's traveling salesman
- Quantitative comparisons of multiscale geometric properties
- Effective Reifenberg theorems in Hilbert and Banach spaces
- Hölder curves and parameterizations in the Analyst's traveling salesman theorem
- Geometry of measures in real dimensions via Hölder parameterizations
- The traveling salesman theorem for Jordan curves
- How to take shortcuts in Euclidean space: making a given set into a short quasi-convex set
- Characterizations of rectifiable metric measure spaces
- The Trouble with von Koch Curves Built from <em>n</em>gons
- Reifenberg parameterizations for sets with holes
- LOCAL SET APPROXIMATION: MATTILA–VUORINEN TYPE SETS, REIFENBERG TYPE SETS, AND TANGENT SETS
- On Besicovitch's ½-Problem
- On the moduli of convexity and smoothness
- Weak Parallelogram Laws for Banach Spaces
- Rectifiable Metric Spaces: Local Structure and Regularity of the Hausdorff Measure
- Optimal weak parallelogram constants for L^p spaces
- Menger curvature and Lipschitz parametrizations in metric spaces
- Characterization of Subsets of Rectifiable Curves in R n
- Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
- The power of backtracking and the confinement of length
- Wild examples of countably rectifiable sets
- Radon measures and Lipschitz graphs
- Sufficient conditions for C^1,α parametrization and rectifiability
- The analyst's traveling salesman theorem in graph inverse limits
- Structure of measures in Lipschitz differentiability spaces
- Positivity of duality mappings
- A Weak Parallelogram Law for l p
- The dimension of the Brownian frontier is greater than 1
- Subsets of rectifiable curves in Banach spaces. II: Universal estimates for almost flat arcs
- Stratified β$\beta$‐numbers and traveling salesman in Carnot groups
This page was built for publication: Subsets of rectifiable curves in Banach spaces. I: Sharp exponents in traveling salesman theorems
