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@weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0512208 or http://arXiv.org/abs/math.FA/0512208 or by email in unzipped form by transmitting an empty message with subject line uget 0512208 or in gzipped form by using subject line get 0512208 to: math@arXiv.org.