Sections and projections of \(L_p\)-zonoids and their polars (Q1742949)

The authors consider \(L_p\)-zonoids and their polars, as introduced by Schneider \(\&\) Weil, and thoroughly investigated by Lutwak et al. A series of papers by Ball, Barthe, \(\&\) Lutwak et al. provide sharp upper and lower estimates for the volumes of \(L_p\)-zonoids and their polars, under the assumption that their generating measure is even and isotropic. In this paper, the authors establish the sharp upper and lower bounds for the volume of \(k\)-dimensional projections (or sections) of \(L_p\)-zonoids and their polars, with even isotropic generating measures.