Hermitian integral geometry

• 成果类型: Article
• 署名作者: Bernig, Andreas; Fu, Joseph H. G.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.2.7
• 发表日期: 2011
• 页码: 907-945
• 关键词: hard lefschetz theorem; multiplicative structure; VALUATIONS; MANIFOLDS; SPACES

摘要

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.