The surface measure and cone measure on the sphere of

Author:
Assaf Naor

Journal:
Trans. Amer. Math. Soc. **359** (2007), 1045-1079

MSC (2000):
Primary 52A20, 60B11

Published electronically:
September 11, 2006

MathSciNet review:
2262841

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a concentration inequality for the norm on the sphere for . This inequality, which generalizes results of Schechtman and Zinn (2000), is used to study the distance between the cone measure and surface measure on the sphere of . In particular, we obtain a significant strengthening of the inequality derived by Naor and Romik (2003), and calculate the precise dependence of the constants that appeared there on .

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Additional Information

**Assaf Naor**

Affiliation:
Department of Mathematics, Hebrew University, Givaat-Ram, Jerusalem, Israel

Address at time of publication:
Microsoft Research, One Microsoft Way, Redmond, Washington 98052-6399

Email:
anaor@microsoft.com

DOI:
https://doi.org/10.1090/S0002-9947-06-03939-0

Keywords:
Geometry of $\ell_p^n$,
cone measure,
surface measure,
concentration inequalities,
convex geometry

Received by editor(s):
May 14, 2001

Received by editor(s) in revised form:
November 22, 2004

Published electronically:
September 11, 2006

Additional Notes:
This work was partially supported by BSF and the Clore Foundation, and is part of the author’s Ph.D. thesis prepared under the supervision of Professor Joram Lindenstrauss.

Article copyright:
© Copyright 2006
American Mathematical Society