Continuous rotation invariant valuations on convex sets
Metric Geometry
2016-09-07 v1
Abstract
The famous Hadwiger theorem classifies all rigid motion invariant continuous valuations on convex sets as linear conbinations of quermassintegrals. We prove much more general result. We classify continuous valuations which are invariant with respect to the orthogonal (or special orthogonal) group. Some applications to integral geometry are given.
Cite
@article{arxiv.math/9905204,
title = {Continuous rotation invariant valuations on convex sets},
author = {Semyon Alesker},
journal= {arXiv preprint arXiv:math/9905204},
year = {2016}
}
Comments
29 pages, published version, abstract added in migration