Hard Lefschetz theorem for valuations and related questions of integral geometry

Semyon Alesker

Hard Lefschetz theorem for valuations and related questions of integral geometry

Metric Geometry 2007-05-23 v3 Differential Geometry

Authors: Semyon Alesker

Abstract

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.

Keywords

valuations hard lefschetz theorem convex sets integral geometry translation invariant even and odd valuations

Cite

@article{arxiv.math/0306137,
  title  = {Hard Lefschetz theorem for valuations and related questions of integral geometry},
  author = {Semyon Alesker},
  journal= {arXiv preprint arXiv:math/0306137},
  year   = {2007}
}

Comments

14 pages, revised version

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