Abstract
The decomposition of the space of continuous and translation-invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger-type theorem for continuous translation-invariant and SO(n)-equivariant tensor valuations is also given. As an application, symmetry properties of rigid-motion invariant and homogeneous bivaluations are established and then used to prove new inequalities of Brunn-Minkowski type for convex body valued valuations.
Original language | English |
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Pages (from-to) | 751-773 |
Number of pages | 23 |
Journal | Geometric and Functional Analysis |
Volume | 21 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2011 |
Keywords
- Valuation
- algebraic integral geometry
- isoperimetric inequality
- tensor valuation
All Science Journal Classification (ASJC) codes
- Analysis
- Geometry and Topology