Local $L^p$-Brunn-Minkowski Inequalities for $p
Title | Local $L^p$-Brunn-Minkowski Inequalities for $p PDF eBook |
Author | Alexander V. Kolesnikov |
Publisher | American Mathematical Society |
Pages | 78 |
Release | 2022-05-24 |
Genre | Mathematics |
ISBN | 1470451603 |
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The Brunn-Minkowski Inequality for P-capacity of Convex Bodies
Title | The Brunn-Minkowski Inequality for P-capacity of Convex Bodies PDF eBook |
Author | Andrea Colesanti |
Publisher | |
Pages | 19 |
Release | 2002 |
Genre | |
ISBN |
Convex Bodies: The Brunn–Minkowski Theory
Title | Convex Bodies: The Brunn–Minkowski Theory PDF eBook |
Author | Rolf Schneider |
Publisher | Cambridge University Press |
Pages | 759 |
Release | 2014 |
Genre | Mathematics |
ISBN | 1107601010 |
A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Theory of Convex Bodies
Title | Theory of Convex Bodies PDF eBook |
Author | Tommy Bonnesen |
Publisher | |
Pages | 192 |
Release | 1987 |
Genre | Mathematics |
ISBN |
Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting
Title | Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting PDF eBook |
Author | Yongsheng Han |
Publisher | American Mathematical Society |
Pages | 118 |
Release | 2022-08-31 |
Genre | Mathematics |
ISBN | 1470453452 |
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Asymptotic Geometric Analysis, Part I
Title | Asymptotic Geometric Analysis, Part I PDF eBook |
Author | Shiri Artstein-Avidan |
Publisher | American Mathematical Soc. |
Pages | 473 |
Release | 2015-06-18 |
Genre | Mathematics |
ISBN | 1470421933 |
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.
The Brunn-Minkowski Inequality and Related Results
Title | The Brunn-Minkowski Inequality and Related Results PDF eBook |
Author | Trista A. Mullin |
Publisher | |
Pages | 0 |
Release | 2018 |
Genre | |
ISBN |
The Brunn-Minkowski Inequality is a classical result that compares the volumes of twosets, in particular convex bodies, and the volume of their Minkowski sum. The proof iselegant and the eects are far reaching in mathematics. In this thesis we will examinethe proof of the inequality, and its multiplicative and integral forms. From there wewill explore a few applications and an analog to Brunn's slice theorem. Additionally, wewill look at how the Brunn-Minkowski Inequality can be used to obtain results regardinggeneral log concave measures, isoperimetric inequalities, and spherical concentrations.We will end the journey with a quick look at what can be said about the intersectionbody of a convex body.