A universal Lipschitz extension property of Gromov hyperbolic spaces

DOI10.4171/RMI/517zbMath1153.54012arXivmath/0601205MaRDI QIDQ925112

Alexander Brudnyi, Yuri A. Brudnyi

Publication date: 29 May 2008

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601205

zbMATH Keywords

metric spacehyperbolic spaceuniversal spacedoubling measureLipschitz functionGromov hyperbolic spacedoubling metric spacequasi-isometric embedding\(C\)-isometric embedding\(K\)-uniform measuremetric space of bounded geometrysimultaneous Lipschitz extension

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Harmonic analysis on homogeneous spaces (43A85) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Cites Work

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• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• The Whitney problem of existence of a linear extension operator
• Embeddings of Gromov hyperbolic spaces
• Extending Lipschitz functions via random metric partitions
• Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• An extension of Tietze's theorem
• Metric spaces with linear extensions preserving Lipschitz condition
• Every complete doubling metric space carries a doubling measure
• Lipschitz-free Banach spaces
• Extensions of Lipschitz maps into Hadamard spaces

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