Identifying 1-rectifiable measures in Carnot groups
From MaRDI portal
Publication:6189131
DOI10.1515/agms-2023-0102arXiv2109.06753MaRDI QIDQ6189131
Matthew Badger, Sean Li, Scott Zimmerman
Publication date: 12 January 2024
Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.06753
Harmonic analysis on homogeneous spaces (43A85) Length, area, volume, other geometric measure theory (28A75) Curves in Euclidean and related spaces (53A04) Sub-Riemannian geometry (53C17)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the structure of continua with finite length and Gołąb's semicontinuity theorem
- Multiscale analysis of 1-rectifiable measures. II: Characterizations
- A counterexample for the geometric traveling salesman problem in the Heisenberg group
- An upper bound for the length of a traveling salesman path in the Heisenberg group
- Rectifiable sets and the traveling salesman problem
- Generalized rectifiability of measures and the identification problem
- Morceaux de graphes lipschitziens et intégrales singulières sur une surface
- Subsets of rectifiable curves in Hilbert space-the analyst's TSP
- Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
- Lectures on analysis on metric spaces
- The traveling salesman theorem in Carnot groups
- Boundedness of the density normalised Jones' square function does not imply 1-rectifiability
- An analyst's traveling salesman theorem for sets of dimension larger than one
- The density theorem and Hausdorff inequality for packing measure in general metric spaces
- 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
- Characterising rectifiable metric spaces using tangent spaces
- The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
- On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion
- On rectifiable measures in Carnot groups: existence of density
- Box-counting by Hölder's traveling salesman
- Purely unrectifiable metric spaces and perturbations of Lipschitz functions
- Effective Reifenberg theorems in Hilbert and Banach spaces
- Multiscale analysis of 1-rectifiable measures: necessary conditions
- Hölder curves and parameterizations in the Analyst's traveling salesman theorem
- Geometry of measures in real dimensions via Hölder parameterizations
- The geometric traveling salesman problem in the Heisenberg group
- Rectifiable sets, densities and tangent measures
- A characterization of 1-rectifiable doubling measures with connected supports
- On rectifiable measures in Carnot groups: representation
- Dimension of a measure
- The traveling salesman problem in the Heisenberg group: Upper bounding curvature
- Two sufficient conditions for rectifiable measures
- Existence of doubling measures via generalised nested cubes
- What is a cube?
- Characterizations of rectifiable metric measure spaces
- A smooth subadditive homogeneous norm on a homogeneous group
- A doubling measure on $\mathbb {R}^d$ can charge a rectifiable curve
- Upper conical density results for general measures on ℝn
- Stratified Lie Groups and Potential Theory for their Sub-Laplacians
- k-Dimensional Regularity Classifications for s-Fractals
- Quantifying curvelike structures of measures by usingL2 Jones quantities
- Menger curvature and Lipschitz parametrizations in metric spaces
- Characterization of Subsets of Rectifiable Curves in R n
- A T(b) theorem with remarks on analytic capacity and the Cauchy integral
- Radon measures and Lipschitz graphs
- Rectifiability
- A New Theory of Dimension
- The φ Rectifiable Subsets of the Plane
- Subsets of rectifiable curves in Banach spaces. I: Sharp exponents in traveling salesman theorems
- Subsets of rectifiable curves in Banach spaces. II: Universal estimates for almost flat arcs
- Stratified β$\beta$‐numbers and traveling salesman in Carnot groups