Theory of valuations on manifolds, I. Linear spaces

Details Theory of valuations on manifolds, I. Linear spaces Theory of valuations on manifolds, I. Linear spaces

2005-03-19

arxiv.org/abs/math/0503397v2

Israel J. Math. 156 (2006), 311--339

Mathematics

Metric Geometry

24 pages, revised version

Scientific paper

This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of a linear space. In this article we still work only with linear spaces. We introduce a space of smooth (non-translation invariant) valuations on a finite dimensional linear space. We present three descriptions of this space. We describe the canonical multiplicative structure on it generalizing the results for polynomial valuations obtained by the author in Geom. Funct. Anal. 14 (2004).

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