Convexity from the Geometric Point of View
Springer International Publishing (Verlag)
978-3-031-50506-5 (ISBN)
Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Vitor Balestro is a Professor of Mathematics at Federal Fluminense University in Niterói, Brazil. He received his PhD in Mathematics from the same university in 2016. In Mathematics, his research interests include convex geometry, geometry of finite dimensional normed spaces, convex analysis and functional analysis. Outside of Mathematics, his main interests are computer programming, computer science, music, and literature.
Horst Martini Before his retirement in 2020, Horst Martini was Full Professor of Mathematics at the Chemnitz University of Technology in Germany (Chair of Geometry). After receiving his Ph.D. in Dresden, in 1988 he obtained his habilitation from the University of Jena, and in 1993 he received his position in Chemnitz. His research interests include convex geometry, discrete geometry, functional analysis, and classical subfields of geometry, as well as applications in optimization and related fields. He also studies certain fields in history of mathematics. For about fifteen years he was editor in chief f the Springer journal Contributions to Algebra and Geometry, and in 2015 he received an honorary professorship from the Harbin University f Science and Technology (China). His passions include travelling to interesting places of geographical and historical significance and studying different genres of good music.
Ralph Teixeira is a Professor of Mathematics at Federal Fluminense University in Niterói, Brazil. He received his PhD in Mathematics from Harvard University in 1998, and has since worked in many areas, including Mathematics applied to Computer Vision, Differential and Discrete Geometry, and lately Convex Geometry. Second to his wife, his main love is computer gaming, but he would never admit this in public.
Preface.- 1. Convex functions.- 2. Convex sets.- 3. A first look into polytopes.- 4. Volume and area.- 5. Classical inequalities.- 6. Mixed volumes- 7. Mixed surface area measures.- 8. The Alexandrov-Frechel inequality.- 9. Affine convex geometry Part 1.- 10. Affine convex geometry Part 2.- 11. Further selected topics.-12. Historical steps of development of convexity as a field.- A. Measure theory for convex geometers.- References.- Index.
| Erscheinungsdatum | 10.05.2024 |
|---|---|
| Reihe/Serie | Cornerstones |
| Zusatzinfo | XIX, 1184 p. 86 illus., 13 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Affine position • asymptotic geometric analysis • Convex body • convex polytope • geometric inequalities |
| ISBN-10 | 3-031-50506-9 / 3031505069 |
| ISBN-13 | 978-3-031-50506-5 / 9783031505065 |
| Zustand | Neuware |
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