Analytic Aspects of Convexity

Description

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. Front Matter ....Pages i-ix Dual Curvature Measures in Hermitian Integral Geometry (Andreas Bernig, Joseph H. G. Fu, Gil Solanes)....Pages 1-17 Estimates for the Integrals of Powered i-th Mean Curvatures (María A. Hernández Cifre, David Alonso-Gutiérrez)....Pages 19-37 Crofton Formulae for Tensorial Curvature Measures: The General Case (Daniel Hug, Jan A. Weis)....Pages 39-60 Extensions of Reverse Volume Difference Inequalities (Alexander Koldobsky, Denghui Wu)....Pages 61-71 Around the Simplex Mean Width Conjecture (Alexander E. Litvak)....Pages 73-84 Discrete Centro-Affine Curvature for Convex Polygons (Alina Stancu)....Pages 85-101 Characterizing the Volume via a Brunn-Minkowski Type Inequality (Jesús Yepes Nicolás)....Pages 103-120