Continuous rotation invariant valuations on convex sets
度量几何
2016-09-07 v1
摘要
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.
引用
@article{arxiv.math/9905204,
title = {Continuous rotation invariant valuations on convex sets},
author = {Semyon Alesker},
journal= {arXiv preprint arXiv:math/9905204},
year = {2016}
}
备注
29 pages, published version, abstract added in migration