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Powers of convex bodies

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Convex and discrete geometry; Geometry; Discrete mathematics

video/mp4

Author affiliation: University of Minnesota

2017-11-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63645

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/