On the spherical Steiner formula

Dr Martin Lotz (University of Manchester)

Frank Adams Room 1,

The spherical Steiner formula expresses a neighbourhood of a (geodesically) convex body on the sphere as a function of certain curvature invariants, the intrinsic volumes of the set. We discuss some surprising properties of these invariants that differ from the Euclidean setting. Among other things, these invariants form a discrete probability distribution that satisfies some sharp concentration of measure phenomenon, and in a certain sense approaches a normal distribution in high dimensions.
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