Download or read book The Determination of Convex Bodies from Geometric Averages of Their Projections and Associated Stability Results written by Karla K. Spriestersbach and published by . This book was released on 1995 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Convex Geometry written by Bozzano G Luisa and published by Elsevier. This book was released on 2014-06-28 with total page 803 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.
Download or read book Research Report written by Markus Kiderlen and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Geometric Analysis written by Keith M. Ball and published by Cambridge University Press. This book was released on 1999-01-28 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.
Download or read book Stability Results for Convex Bodies in Geometric Tomography written by Markus Kiderlen and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by H. Groemer and published by Cambridge University Press. This book was released on 1996-09-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.
Download or read book Geometric Tomography written by Richard J. Gardner and published by Cambridge University Press. This book was released on 2006-06-19 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: seventy-two unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. This comprehensive work will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
Download or read book Lectures on Convex Geometry written by Daniel Hug and published by Springer Nature. This book was released on 2020-08-27 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Download or read book The Interface Between Convex Geometry and Harmonic Analysis written by Alexander Koldobsky and published by American Mathematical Soc.. This book was released on 2008 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the modern results of convex geometry using harmonic analysis outlines the development of Fourier analysis and how its methods are used to solve geometric problems. The book includes new results since a previous book from the author in 2005. The material is presented in lecture format, with the first section of each lecture offering an accessible snapshot for novice readers.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2004 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convexity from the Geometric Point of View written by Vitor Balestro and published by Springer Nature. This book was released on with total page 1195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex and Fractal Geometry written by Robert J. MacG. Dawson and published by . This book was released on 2009 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference Convex and Fractal Geometry was held at the Stefan Banach International Mathematical Center at Bedlewo, May 21-26, 2007. ... This volume contains twelve papers related to the talks delivered at that conference.
Download or read book Stability Results in Reconstructing Convex Bodies from Projections written by Marco Longinetti and published by . This book was released on 1984 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Structural Results for Convex Bodies written by Victor Glasgo and published by . This book was released on 2020 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with topics in convex geometry. In the first part, we define a new class of convex bodies, the gravitational illumination bodies. We prove some properties of the gravitational illumination bodies. The main theorems relate gravitational illumination bodies to quantities in affine differential geometry, the affine surface area and p-affine surface area. In chapter 1, we gather notation and give background material from analysis and convex geometry. In chapter 2, we define the gravitational illumination body of a convex body and state our main theorems. In chapter 3 we compute the gravitational illumination body for the Euclidean ball and consider the case of polytopes. In chapter 4 we prove properties of the gravitational illumination body. In chapters 5 and 6 we prove our main results. In the second part, we show a stability result for floating bodies in terms of the Hausdorff metric and the Florian metric. It is an open problem whether the same convex body can be the floating body of two different bodies. A corollary of the stability result, yields that this is only possible if the original bodies are close. In chapter 7, we state and prove our main theorems on the stability of floating bodies.
Download or read book Advances In Theory And Applications Of Random Sets Proceedings Of The Symposium written by Dominique Jeulin and published by World Scientific. This book was released on 1997-01-16 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers topics ranging from pure and applied mathematics to pedagogical issues in mathematics. There are papers in mathematical biology, differential equations, difference equations, dynamical systems, orthogonal polynomials, topology, calculus reform, algebra, and numerical analysis. Most of the papers include new, interesting results that are at the cutting edge of the respective subjects. However, there are some papers of an expository nature.
Download or read book Mathematika written by and published by . This book was released on 1997 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: A journal of pure and applied mathematics.
Download or read book Asymptotic Geometric Analysis Part I written by Shiri Artstein-Avidan and published by American Mathematical Soc.. This book was released on 2015-06-18 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
