An Elementary Introduction to Modern Convex Geometry

作者: Keith M. Ball

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摘要: Preface 1 Lecture 1. Basic Notions 2 2. Spherical Sections of the Cube 8 3. Fritz John’s Theorem 13 4. Volume Ratios and Octahedron 19 5. The Brunn–Minkowski Inequality Its Extensions 25 6. Convolutions Ratios: Reverse Isoperimetric Problem 32 7. Central Limit Large Deviation Inequalities 37 8. Concentration Measure in Geometry 41 9. Dvoretzky’s 47 Acknowledgements 53 References Index 55

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