Local Lp Brunn Minkowski Inequalities For P
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Author | : Alexander V. Kolesnikov |
Publisher | : American Mathematical Society |
Total Pages | : 78 |
Release | : 2022-05-24 |
Genre | : Mathematics |
ISBN | : 1470451603 |
Download Local $L^p$-Brunn-Minkowski Inequalities for $p Book in PDF, Epub and Kindle
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Author | : Andrea Colesanti |
Publisher | : |
Total Pages | : 19 |
Release | : 2002 |
Genre | : |
ISBN | : |
Download The Brunn-Minkowski Inequality for P-capacity of Convex Bodies Book in PDF, Epub and Kindle
Author | : Yongsheng Han |
Publisher | : American Mathematical Society |
Total Pages | : 118 |
Release | : 2022-08-31 |
Genre | : Mathematics |
ISBN | : 1470453452 |
Download Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting Book in PDF, Epub and Kindle
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Author | : Rolf Schneider |
Publisher | : Cambridge University Press |
Total Pages | : 759 |
Release | : 2014 |
Genre | : Mathematics |
ISBN | : 1107601010 |
Download Convex Bodies: The Brunn–Minkowski Theory Book in PDF, Epub and Kindle
A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Author | : Tommy Bonnesen |
Publisher | : |
Total Pages | : 192 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : |
Download Theory of Convex Bodies Book in PDF, Epub and Kindle
Author | : Trista A. Mullin |
Publisher | : |
Total Pages | : 0 |
Release | : 2018 |
Genre | : |
ISBN | : |
Download The Brunn-Minkowski Inequality and Related Results Book in PDF, Epub and Kindle
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.
Author | : Ronen Eldan |
Publisher | : Springer Nature |
Total Pages | : 443 |
Release | : 2023-11-01 |
Genre | : Mathematics |
ISBN | : 3031263006 |
Download Geometric Aspects of Functional Analysis Book in PDF, Epub and Kindle
This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
Author | : Shiri Artstein-Avidan |
Publisher | : American Mathematical Soc. |
Total Pages | : 473 |
Release | : 2015-06-18 |
Genre | : Mathematics |
ISBN | : 1470421933 |
Download Asymptotic Geometric Analysis, Part I Book in PDF, Epub and Kindle
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.
Author | : Alexander Koldobsky |
Publisher | : American Mathematical Soc. |
Total Pages | : 178 |
Release | : 2014-11-12 |
Genre | : Mathematics |
ISBN | : 1470419521 |
Download Fourier Analysis in Convex Geometry Book in PDF, Epub and Kindle
The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.
Author | : Chris Kottke |
Publisher | : American Mathematical Society |
Total Pages | : 124 |
Release | : 2022-11-10 |
Genre | : Mathematics |
ISBN | : 1470455412 |
Download Partial Compactification of Monopoles and Metric Asymptotics Book in PDF, Epub and Kindle
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