Convex and Discrete Geometry

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Springer Science & Business Media, May 17, 2007 - Mathematics - 580 pages

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an 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. It should also be of use to people working in other areas of mathematics and in the applied fields.

 

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Contents

Preface Convex Functions 1 Convex Functions of One Variable
1
10
37
Convex Bodies 3 Convex Sets Convex Bodies and Convex Hulls
41
11
60
Mixed Volumes and Quermassintegrals
79
Valuations
110
The BrunnMinkowski Inequality
141
Symmetrization
168
12
381
16
416
20
429
27
442
32
450
34
499
References
513
35
514

Inequality
185
The Space of Convex Bodies
230
Convex Polytopes
243
Geometry of Numbers and Aspects of Discrete Geometry 353
352
Index
567
Author Index
577
Copyright

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About the author (2007)

1959-66 Study of mathematics and physics, Univ Vienna, Univ Kansas

1996 PhD, Univ Vienna

1966-71 Assistant, Techn.Univ.Vienna

1968 Award of the ÖMG

1969 (Junior) Kardinal Innitzer Award

1970- Docent, Techn. Univ. Vienna

1971-76 Full Professor of Mathematics, Univ. Linz

1976- Full Professor of Mathematical Analysis, Techn. Univ. Vienna

1978-82 President, Austrian Math. Soc.

1981-87 Head, Division of Mathematics, Techn. Univ. Vienna

1985 Hon.Member, Accademia Nazionale di Scienze, Letter e Arti, Modena

1988 Corr. Member, Austrian Academy of Sciences

1991 Full Member, Austrian Academy of Sciences

2000 Hon. Doctorate, Univ. Turin

2001 Hon. Doctorate, Univ. Siegen

2001 Memorial Medal, Fac. Math and Physics, Charles Univ. Prague

2002 Korr. Member, Bayer. Akad. Wiss.

2003 Foreign Member, Russia Acad. Sciences

More than 100 articles and books in the geometry of numbers, convex and discrete geometry, and analysis. Extended visits to Budapest, Bologna, Toronto, Hobart (Tasmania), Chandigarh, Turin, Messina, Moscow-St.Petersburg, Warsaw, Sofia, Guanajuato, Peking, Tel Aviv-Jerusalem, Vancouver, Heraklion, Alicante.

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