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The surface measure and cone measure on the sphere of  |
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| Authors: | Assaf Naor |
| Institution: | Department of Mathematics, Hebrew University, Givaat-Ram, Jerusalem, Israel |
| 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  . |
| Keywords: | Geometry of $\ell_p^n$ cone measure surface measure concentration inequalities convex geometry |
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