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Analytic Aspects of Convexity

  • Book
  • © 2018

Overview

Editors:
  1. Gabriele Bianchi

    1. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

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  2. Andrea Colesanti

    1. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

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  3. Paolo Gronchi

    1. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

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  • 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

Part of the book series: Springer INdAM Series (SINDAMS, volume 25)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Dual Curvature Measures in Hermitian Integral Geometry

    • Andreas Bernig, Joseph H. G. Fu, Gil Solanes
    Pages 1-17

  3. Estimates for the Integrals of Powered i-th Mean Curvatures

    • María A. Hernández Cifre, David Alonso-Gutiérrez
    Pages 19-37

  4. Crofton Formulae for Tensorial Curvature Measures: The General Case

    • Daniel Hug, Jan A. Weis
    Pages 39-60

  5. Extensions of Reverse Volume Difference Inequalities

    • Alexander Koldobsky, Denghui Wu
    Pages 61-71

  6. Around the Simplex Mean Width Conjecture

    • Alexander E. Litvak
    Pages 73-84

  7. Discrete Centro-Affine Curvature for Convex Polygons

    • Alina Stancu
    Pages 85-101

  8. Characterizing the Volume via a Brunn-Minkowski Type Inequality

    • Jesús Yepes Nicolás
    Pages 103-120
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About this book

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.

Editors and Affiliations

  • Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

    Gabriele Bianchi, Andrea Colesanti, Paolo Gronchi

About the editors

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.

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