Mixed volumes that is typically proved in a separate context. Keywords: Polytope; Isoperimetric; Geometric inequality; Minkowski problem; Mixed. Facet normals and facet areas, is there a convex polytope in Rn whose facets fit the. Wills (Eds.), Handbook of Convex Geometry, North-Holland, Amsterdam, 1993, pp. Citation: Proceedings of the CUPM Geometry Conference, Mathematical. Society Conference on Computer Vision and Pattern Recognition, volume 2, pages. Kluwer, 2000.

Author by: Gerard Meurant Language: en Publisher by: Elsevier Format Available: PDF, ePub, Mobi Total Read: 59 Total Download: 501 File Size: 55,6 Mb Description: 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.

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The selection is a valuable source of data for mathematicians and researchers interested in convex geometry. Author by: Language: en Publisher by: Elsevier Format Available: PDF, ePub, Mobi Total Read: 85 Total Download: 880 File Size: 53,5 Mb Description: The Handbook presents an overview of most aspects of modern Banach space theory and its applications.

The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography.

Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory. Author by: Peter Brass Language: en Publisher by: Springer Science & Business Media Format Available: PDF, ePub, Mobi Total Read: 73 Total Download: 882 File Size: 54,6 Mb Description: This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

Author by: Peter M. Gruber Language: en Publisher by: Springer Science & Business Media Format Available: PDF, ePub, Mobi Total Read: 11 Total Download: 583 File Size: 48,7 Mb Description: Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields. Author by: Alexander Koldobsky Language: en Publisher by: American Mathematical Soc. Format Available: PDF, ePub, Mobi Total Read: 84 Total Download: 307 File Size: 47,7 Mb Description: 'The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, rather than to dwell on technical difficulties.