Lefschetz theorem for valuations and related questions of integral geometry
نویسنده
چکیده
We continue studying the properties of the multiplicative structure on valuations. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss problems of integral geometry staying behind these properties. Then we formulate a conjectural analogue of this result for odd valuations.
منابع مشابه
Lefschetz theorem for valuations , complex integral geometry , and unitarily invariant valuations
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 genera...
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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 genera...
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