This is an announcement for the paper "Inequalities for mixed $p$-affine surface area" by Elisabeth Werner and Deping Ye.

Abstract: We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed $p$-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of $L_p$ affine surface areas, mixed $p$-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 52A20, 53A15

Remarks: 39 pages

The source file(s), MixedLp.tex: 97032 bytes, is(are) stored in gzipped form as 0812.4550.gz with size 26kb. The corresponding postcript file has gzipped size 162kb.

Submitted from: elisabeth.werner@case.edu

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