TY - JOUR
T1 - Isomorphic Steiner symmetrization
AU - Klartag, B.
AU - Milman, V. D.
PY - 2003
Y1 - 2003
N2 - This paper proves that there exist 3n Steiner symmetrizations that transform any convex set K ⊂ ℝn into an isomorphic Euclidean ball; i.e. if vol(K) = vol(Dn) where Dn is the standard Euclidean unit ball, then K can be transformed into a body K̃ such that c1Dn ⊂ K̃ ⊂ c2D n, where c1, c2 are numerical constants. Moreover, for any c > 2, cn symmetrizations are also enough.
AB - This paper proves that there exist 3n Steiner symmetrizations that transform any convex set K ⊂ ℝn into an isomorphic Euclidean ball; i.e. if vol(K) = vol(Dn) where Dn is the standard Euclidean unit ball, then K can be transformed into a body K̃ such that c1Dn ⊂ K̃ ⊂ c2D n, where c1, c2 are numerical constants. Moreover, for any c > 2, cn symmetrizations are also enough.
UR - http://www.scopus.com/inward/record.url?scp=0042916447&partnerID=8YFLogxK
U2 - 10.1007/s00222-003-0290-y
DO - 10.1007/s00222-003-0290-y
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AN - SCOPUS:0042916447
SN - 0020-9910
VL - 153
SP - 463
EP - 485
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -