Some Applications of Ball’s Extension Theorem
نویسنده
چکیده
We present two applications Ball’s extension theorem. First we observe that Ball’s extension theorem, together with the recent solution of Ball’s Markov type 2 problem due to Naor, Peres, Schramm and Sheffilield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Secondly, we prove that the distortion required to embed the integer lattice {0, 1, . . . , m}n, equipped with the `p metric, in any 2-uniformly convex Banach space is of order min { n 1 2− 1 p , m1− 2 p } .
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