The product on smooth and generalized valuations

Semyon Alesker*, Andreas Bernig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms, and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to transversal intersections. This result is used to prove a general kinematic formula on compact rank one symmetric spaces.

Original languageEnglish
Pages (from-to)507-560
Number of pages54
JournalAmerican Journal of Mathematics
Issue number2
StatePublished - Apr 2012


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