1 Dual curvature measures in Hermitian integral geometry, A. Bernig, J. H. G. Fu and G. Solanes -- 2 Estimates for the integrals of powered i-th mean curvatures, M. H. Hernandez Cifre and D. Alonso-Gutierrez -- 3 Crofton formulae for tensorial curvature measures: the general case, D. Hug and J. A. Weis -- 4 Extensions of reverse volume difference inequalities, A. Koldobsky and D. Wu -- 5 Around the simplex mean width conjecture, A. Litvak -- 6 Discrete centro-affine curvatures for convex polygons, A. Stancu -- 7 Characterizing the volume via a Brunn-Minkowski inequality, J. Yepes-Nicolas.

This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world's leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.