Hermitian integral geometry

Details Hermitian integral geometry Hermitian integral geometry

2008-01-04

arxiv.org/abs/0801.0711v9

Ann. of Math. 173 (2011), 907-945

Mathematics

Differential Geometry

To appear in Ann. of Math. Version for publication

Scientific paper

We give in explicit form the principal kinematic formula for the action of the affine unitary group on $\C^n$, together with a straightforward algebraic method for computing the full array of unitary kinematic formulas, expressed in terms of certain convex valuations introduced, essentially, by H. Tasaki. We introduce also several other canonical bases for the algebra of unitary-invariant valuations, explore their interrelations, and characterize in these terms the cones of positive and monotone elements.

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