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.

Highlights recent advances in those areas of Convex Geometry that are currently most intensively researched Includes contributions by the leading experts in the field Presents open problems that can be of great interest to young researchers

Autorentext
Gabriele Bianchi, Andrea Colesanti and Paolo Gronchi are professors at the Department of Mathematics and Computer Science of the University of Florence. Their main research interest is in the analytic aspects of Convex Geometry.

Inhalt

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.