Interaction of Order and Convexity

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Interaction ofOrder and Convexity

• S.S. Kutateladze

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The Gift of Mathematics

• 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.

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Alexandrov (1912-1999)

• Alexandr Danilovich Alexandrov was the first and
  foremost Russian geometer of the twentieth
  century.
• He contributed to mathematics under the slogan
• Retreat to Euclid.

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His Contribution
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Abstract Convexity
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H-Convexity
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Hyperspaces
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ReshetnyaksTheorem
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Choquet Theory
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Majorization
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Alexandrovs Theorem
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Dual Hyperspace
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Identification
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Blaschkes Sum
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Mixed Volume as Duality
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Dual Cones
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Decomposition and Inclusion
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Isoperimetric-Type Problems
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ProblemsIngredients
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Convex Problems
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Soap Bubbles
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External Problems
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Uryhson-TypeProblems
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Current Hyperplanes