Open Access
March 2006 Structure of the unitary valuation algebra
Joseph H.G. Fu
J. Differential Geom. 72(3): 509-533 (March 2006). DOI: 10.4310/jdg/1143593748


S. Alesker has shown that if G is a compact subgroup of O(n) acting transitively on the unit sphere Sn-1, then the vector space ValG of continuous, translation-invariant, G-invariant convex valuations on Rn has the structure of a finite dimensional graded algebra over R satisfying Poincaré duality. We show that the kinematic formulas for G are determined by the product pairing. Using this result we then show that the algebra ValU(n) is isomorphic to R[s, t]/(fn+1, fn+2), where s, t have degrees 2 and 1 respectively, and the polynomial fi is the degree i term of the power series log(1 + s + t).


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Joseph H.G. Fu. "Structure of the unitary valuation algebra." J. Differential Geom. 72 (3) 509 - 533, March 2006.


Published: March 2006
First available in Project Euclid: 28 March 2006

zbMATH: 1096.52003
MathSciNet: MR2219942
Digital Object Identifier: 10.4310/jdg/1143593748

Rights: Copyright © 2006 Lehigh University

Vol.72 • No. 3 • March 2006
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