TY - JOUR
T1 - Some applications of ball's extension theorem
AU - Mendel, Manor
AU - Naor, Assaf
PY - 2006/9
Y1 - 2006/9
N2 - We present two applications of 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 Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice {0,1,..., m} n, equipped with the ℓ p n metric, in any 2-uniformly convex Banach space is of order min {n 1/2-1/p, m 1-2/p}.
AB - We present two applications of 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 Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice {0,1,..., m} n, equipped with the ℓ p n metric, in any 2-uniformly convex Banach space is of order min {n 1/2-1/p, m 1-2/p}.
KW - Bi-Lipschitz embeddings
KW - Lipschitz extension
UR - http://www.scopus.com/inward/record.url?scp=33748354258&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-06-08298-0
DO - 10.1090/S0002-9939-06-08298-0
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AN - SCOPUS:33748354258
SN - 0002-9939
VL - 134
SP - 2577
EP - 2584
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -