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Interaction of Order and Convexity

Interaction of Order and Convexity. S.S. Kutateladze. Mathematics is not a divine gift. Mathematics is a human enterprise, challenge, and endeavor. The gift of mathematics goes from master to student. The alternating chain of masters and students is the true savior of mathematics.

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Interaction of Order and Convexity

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  1. Interaction ofOrder and Convexity S.S. Kutateladze

  2. Mathematics is not a divine gift. Mathematics is a human enterprise, challenge, and endeavor. The gift of mathematics goes from master to student. The alternating chain of masters and students is the true savior of mathematics. • Geometry is a vast treasure trove founded by Euclid and enriched by his innumerous students and followers. Alexandr Alexandrov was one of them. The Gift of Mathematics

  3. Alexandr Danilovich Alexandrov was the first and foremost Russian geometer of the twentieth century. • He contributed to mathematics under the slogan: • “Retreat to Euclid.’’ Alexandrov(1912-1999)

  4. His Contribution

  5. Abstract Convexity

  6. H-Convexity

  7. Hyperspaces

  8. Reshetnyak’sTheorem

  9. Choquet Theory

  10. Majorization

  11. Alexandrov’s Theorem

  12. Dual Hyperspace

  13. Identification

  14. Blaschke’s Sum

  15. Mixed Volume as Duality

  16. Dual Cones

  17. Decomposition and Inclusion

  18. Isoperimetric-Type Problems

  19. Problem’sIngredients

  20. Convex Problems

  21. Soap Bubbles

  22. External Problems

  23. Uryhson-TypeProblems

  24. CurrentHyperplanes

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