Sharp finiteness principles for Lipschitz selections

DOI10.1007/s00039-018-0467-6zbMath1412.46044arXiv1801.00325OpenAlexW2962768597WikidataQ129237682 ScholiaQ129237682MaRDI QIDQ1632236

Pavel Shvartsman, Charles L. Fefferman

Publication date: 13 December 2018

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00325

zbMATH Keywords

set-valued mappingHelly's theoremmetric treeNagata dimensionLipschitz selectionSteiner-type pointWhitney partition

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items

Locally \(C^{1,1}\) convex extensions of \(1\)-jets ⋮ Smooth selection for infinite sets ⋮ \(C^2\) interpolation with range restriction ⋮ Approximating spaces of Nagata dimension zero by weighted trees ⋮ On \(C^m\) solutions to systems of linear inequalities ⋮ \(C^{1, \omega }\) extension formulas for $1$-jets on Hilbert spaces ⋮ On the core of a low dimensional set-valued mapping

Cites Work

• Interpolation of data by smooth nonnegative functions
• Assouad-Nagata dimension via Lipschitz extensions
• Whitney's extension problem for \(C^m\)
• Fitting a \(C^m\)-smooth function to data. II
• Lipschitz selections of set-valued mappings and Helly's theorem
• Barycentric selectors and a Steiner-type point of a convex body in a Banach space
• A sharp form of Whitney's extension theorem
• Fitting a \(C^m\)-smooth function to data. I.
• Fitting a \(C^m\)-smooth function to data. III.
• A generalized sharp Whitney theorem for jets
• Finiteness principles for smooth selection
• Whitney’s extension problem for multivariate 𝐶^{1,𝜔}-functions
• Note on dimension theory for metric spaces
• The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spaces
• Whitney’s extension problems and interpolation of data
• A decomposition of multidimensional point sets with applications to k -nearest-neighbors and n -body potential fields
• The trace of jet space 𝐽^{𝑘}Λ^{𝜔} to an arbitrary closed subset of ℝⁿ
• A Note on the Lipschitz Selection
• Metric dimensions of minor excluded graphs and minor exclusion in groups
• Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
• Methods of Geometric Analysis in Extension and Trace Problems
• On Lipschitz selections of affine-set valued mappings
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