A doubling subset of Lp for p > 2 that is inherently infinite dimensional

Vincent Lafforgue; Assaf Naor

doi:10.1007/s10711-013-9924-4

A doubling subset of L_p for p > 2 that is inherently infinite dimensional

Vincent Lafforgue, Assaf Naor

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

It is shown that for every p∈(2,∞) there exists a doubling subset of L_p that does not admit a bi-Lipschitz embedding into R^k for any k∈N.

Original language	English (US)
Pages (from-to)	387-398
Number of pages	12
Journal	Geometriae Dedicata
Volume	172
Issue number	1
DOIs	https://doi.org/10.1007/s10711-013-9924-4
State	Published - Oct 1 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Doubling metric spaces
Heisenberg group
Metric embeddings

Access to Document

10.1007/s10711-013-9924-4

Cite this

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title = "A doubling subset of Lp for p > 2 that is inherently infinite dimensional",

abstract = "It is shown that for every p∈(2,∞) there exists a doubling subset of Lp that does not admit a bi-Lipschitz embedding into Rk for any k∈N.",

keywords = "Doubling metric spaces, Heisenberg group, Metric embeddings",

author = "Vincent Lafforgue and Assaf Naor",

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AU - Naor, Assaf

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AB - It is shown that for every p∈(2,∞) there exists a doubling subset of Lp that does not admit a bi-Lipschitz embedding into Rk for any k∈N.

KW - Doubling metric spaces

KW - Heisenberg group

KW - Metric embeddings

UR - https://www.scopus.com/pages/publications/84943158130

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JF - Geometriae Dedicata

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