Hard Lefschetz theorem for valuations and related questions of integral geometry

Details Hard Lefschetz theorem for valuations and related questions of integral geometry Hard Lefschetz theorem for valuations and related questions of integral geometry

2003-06-08

arxiv.org/abs/math/0306137v3

Geometric aspects of functional analysis, 9--20, Lecture Notes in Math., 1850, Springer, Berlin, 2004.

Mathematics

Metric Geometry

14 pages, revised version

Scientific paper

We study the properties of the multiplicative structure on valuations on
convex sets. We prove a new version of the hard Lefschetz theorem for even
translation invariant continuous valuations, and discuss related problems of
integral geometry. Then we formulate a conjectural analogue of this result for
odd valuations.

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