This is an announcement for the paper "Shadow systems and volume of polar convex bodies" by Mathieu Meyer and Shlomo Reisner.

Abstract: We prove that the reciprocal of the volume of the polar bodies, about the Santal'o point, of a {\em shadow system/} of convex bodies $K_t$, is a convex function of $t$. Thus extending to the non-symmetric case a result of Campi and Gronchi. The case that the reciprocal of the volume is an affine function of $t$ is also investigated and is characterized under certain conditions. We apply these results to prove exact reverse Santal'o inequality for polytopes in $\rd{d}$ that have at most $d+3$ vertices.

Archive classification: Functional Analysis

Remarks: to appear in Mathematika

The source file(s), MMSR.tex: 55818 bytes, is(are) stored in gzipped form as 0606305.gz with size 18kb. The corresponding postcript file has gzipped size 93kb.

Submitted from: reisner@math.haifa.ac.il

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/math.FA/0606305

or

http://arXiv.org/abs/math.FA/0606305

or by email in unzipped form by transmitting an empty message with subject line

uget 0606305

or in gzipped form by using subject line

get 0606305

to: math@arXiv.org.