The product on smooth and generalized valuations
Metric Geometry
2013-11-19 v4 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0904.1347,
title = {The product on smooth and generalized valuations},
author = {Semyon Alesker and Andreas Bernig},
journal= {arXiv preprint arXiv:0904.1347},
year = {2013}
}
Comments
50 pages; in Theorem 8.3 the statement of separate continuity of product on generalized valuations with given wave front sets is replaced by joint sequential continuity. Appropriate corrections have been made in few other places of the paper