Skip to content
DraconiticResearch
Search Sources API
190,869 studies31 sourcesUpdated 5 min ago
PreprintarXiv licencearXiv

Kirszbraun's Intersection Property and Nonexpansive Extensions

  • Valentin Gutev
Open at sourcePDFDOICite

Abstract

This paper aims to present the historical development of the extension problem of nonexpansive maps in Euclidean and Hilbert spaces, and to serve as a comprehensive guide to this specific area. Such extensions are based on a geometric property of the intersection of closed balls in Euclidean spaces, known as the Kirszbraun intersection property. Subsequently, a number of authors have extended this property to Hilbert and other spaces. All these results are discussed in this paper, but the paper itself is not a mechanical compilation of already known proofs. The material has been developed with an emphasis on the natural connections between all these results and the corresponding concepts involved in them. Furthermore, most of these results are presented with new simplified proofs. Last but not least, the paper also contains some new results related to this extension problem.

Related

  1. An unbounded convex set with the fixed point property for nonexpansive mappings
    M. Japón, Javier Laguna-Ricart
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. A property of boundary extensions of atomic singular inner functions
    Iason Efraimidis, Adrian Llinares, Sullivan MacDonald +2
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions
    Daowei Lu, Dingguo Wang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. A Bogomolov property for moduli spaces of polynomials over abelian extensions
    Geng-Rui Zhang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryDynamical systemsarXiv
  5. Wavelet orthonormal bases for nonexpansive dilations
    Jordy Timo van Velthoven, Felix Voigtlaender
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{gutev2026kirszbrauns,
  title = {{Kirszbraun's Intersection Property and Nonexpansive Extensions}},
  author = {Valentin Gutev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28862},
  eprint = {2610.28862},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28862},
}
RIS
TY  - UNPB
TI  - Kirszbraun's Intersection Property and Nonexpansive Extensions
AU  - Valentin Gutev
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28862
UR  - https://arxiv.org/abs/2610.28862
AB  - This paper aims to present the historical development of the extension problem of nonexpansive maps in Euclidean and Hilbert spaces, and to serve as a comprehensive guide to this specific area. Such extensions are based on a geometric property of the intersection of closed balls in Euclidean spaces, known as the Kirszbraun intersection property. Subsequently, a number of authors have extended this property to Hilbert and other spaces. All these results are discussed in this paper, but the paper itself is not a mechanical compilation of already known proofs. The material has been developed with an emphasis on the natural connections between all these results and the corresponding concepts involved in them. Furthermore, most of these results are presented with new simplified proofs. Last but not least, the paper also contains some new results related to this extension problem.
ER  -