A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension

• Autorzy: Guy David , Marie Snipes
• Języki publikacji: EN

Abstrakty

EN

We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.

Słowa kluczowe

EN

Assouad Embedding; doubling metric spaces; snowflake distance

Kategorie tematyczne

• 53C23: Global geometric and topological methods (\`a la Gromov); differential geometric analysis on metric spaces
• 28A75: Length, area, volume, other geometric measure theory
• 54F45: Dimension theory

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 36-41

Daty

otrzymano

2012-11-14

zaakceptowano

2012-12-26

online

2013-01-14

Twórcy

autor

Guy David

• Univ Paris-Sud, Laboratoire de mathématiques UMR-8628,
  Orsay F-91405, France and Institut Universitaire de France

autor

Marie Snipes

• Department of Mathematics, Hayes Hall, Kenyon College,
  Gambier, Ohio 43022, USA

Bibliografia

• P. Assouad, Plongements lipschitziens dans Rn, Bull. Soc. Math. France, 111(4), 429–448, 1983.
• J. Heinonen, Lectures on Analysis on Metric Spaces, Springer-Verlag, 2001.
• A. Naor and O. Neiman, Assouad’s theorem with dimension independent of the snowflaking, Revista Matemática Iberoamericana 28 (4), 1–21, 2012 [WoS]

Identyfikatory

DOI

10.2478/agms-2012-0003