L p Affine Isoperimetric Inequalities

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Star body valued valuations (2009, unknown): “[3], [5], [10], [24], [29], [31], [33], [37].”
Concentration of mass on convex bodies (2006, background): “Lutwak, Yang and Zhang (see [26] and [15] for a different proof) have established the following Lq affine isoperimetric inequality.”
Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach (2011, background): “(3.3) This recovers up to a constant the lower bound of Lutwak, Yang and Zhang (1.5).”
General $L_p$ affine isoperimetric inequalities (2008, methodology): “Lutwak, Yang, and Zhang [ 30 ] (see also Campi and Gronchi [6]) established the Lp version of the Busemann–Petty centroid inequality: For p > 1 and convex bodies K containing the origin in their interiors,”
Ellipsoids and matrix-valued valuations (2003, methodology): “This definition is natural in the framework of the Lp-Brunn-Minkowski and dual Lp-Brunn-Minkowski theory (see [18], [19], [20], [21], [24]); there the ellipsoids Γ2 and Γ−2 are dual notions.”
A characterization of Lp intersection bodies (2006, background): “In particular, Lutwak, Yang, and Zhang introduced Lp projection bodies and obtained important ane isoperimetric inequalities (see [ 30 ], [31]).”
The even Orlicz-Minkowski problem (2010, unknown): “[1–5, 7–10, 12, 13, 15–22, 25–39, 41–44, 47, 49, 50, 52–55, 58, 60–63, 65–68]).”