English

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

R2 v1 2026-06-21T12:49:29.448Z