[Banach] Abstract of a paper by Emanuel Milman

[Dale Alspach]

This is an announcement for the paper "A comment on the low-dimensional
Busemann-Petty problem" by Emanuel Milman.


Abstract: The generalized Busemann-Petty problem asks whether
centrally-symmetric convex bodies having larger volume of all
m-dimensional sections necessarily have larger volume. When m>3
this is known to be false, but the cases m=2,3 are still open. In
those cases, it is shown that when the smaller body's radial function
is a (n-m)-th root of the radial function of a convex body, the
answer to the generalized Busemann-Petty problem is positive (for
any larger star-body). Several immediate corollaries of this
observation are also discussed.

Archive classification: Functional Analysis; Metric Geometry

Remarks: 9 pages, to appear in GAFA Seminar Notes

The source file(s), low-dim-BP-problem.bbl: 4623 bytes,
low-dim-BP-problem.tex: 24305 bytes, is(are) stored in gzipped form
as 0512208.tar.gz with size 10kb. The corresponding postcript file
has gzipped size 53kb.

Submitted from: emanuel.milman at weizmann.ac.il

The paper may be downloaded from the archive by web browser from
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 http://front.math.ucdavis.edu/math.FA/0512208

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 http://arXiv.org/abs/math.FA/0512208

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 to: math at arXiv.org.