BIRS Workshop Lecture Videos
Powers of convex bodies Rotem, Liran
Given a convex body $K$ and a real number $a$, how should we define the convex body $K^a$? One way to answer this question is to write down a list of natural properties we expect from such a power, and then prove existence and uniqueness of a construction satisfying these properties. In this talk we will explain why a natural power operation does not exist for $a > 1$, but does exist for $0 < a < 1$. We will also discuss the uniqueness question, which is more delicate. Based on joint work with Vitali Milman.
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