Abstract
We investigate the effect of a Steiner type symmetrization on the isotropic constant of a convex body. We reduce the problem of bounding the isotropic constant of an arbitrary convex body, to the problem of bounding the isotropic constant of a finite volume ratio body. We also add two observations concerning the slicing problem. The first is the equivalence of the problem to a reverse Brunn-Minkowski inequality in isotropic position. The second is the essential monotonicity in n of where the supremum is taken over all convex bodies in , and L K is the isotropic constant of K.
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© 2004 Springer-Verlag Berlin/Heidelberg
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Bourgain, J., Klartag, B., Milman, V. (2004). Symmetrization and Isotropic Constants of Convex Bodies. In: Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44489-3_10
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DOI: https://doi.org/10.1007/978-3-540-44489-3_10
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22360-3
Online ISBN: 978-3-540-44489-3
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