Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations

Details Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations

2002-09-20

arxiv.org/abs/math/0209263v4

J. Differential Geom. 63 (2003), no. 1, 63--95.

Mathematics

Metric Geometry

33 pages, revised version

Scientific paper

We obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets (a version of the hard Lefschetz theorem). Using these and our previous results we obtain explicit characterization of unitarily invariant translation invariant continuous valuations. It implies new integral geometric formulas for real submanifolds in Hermitian spaces generalizing the classical kinematic formulas in Euclidean spaces due to Poincar\'e, Chern, Santal\'o, and others.

Affiliated with

Also associated with

No associations

Rating

Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-224492