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Harmonic Blaschke–Minkowski Homomorphism.
- Source :
-
Symmetry (20738994) . Jul2022, Vol. 14 Issue 7, pN.PAG-N.PAG. 10p. - Publication Year :
- 2022
-
Abstract
- Centroid bodies are a continuous and G L (n) -contravariant valuation and play critical roles in the solution to the Busemann–Petty problem. In this paper, we introduce the notion of harmonic Blaschke–Minkowski homomorphism and show that such a map is represented by a spherical convolution operator. Furthermore, we consider the Shephard-type problem of whether Φ K ⊆ Φ L implies V (K) ≤ V (L) , where Φ is a harmonic Blaschke–Minkowski homomorphism. Some important results for centroid bodies are extended to a large class of valuations. Finally, we give two interesting results for even and odd harmonic Blaschke–Minkowski homomorphisms, separately. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HOMOMORPHISMS
*CENTROID
*VALUATION
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 14
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 158318533
- Full Text :
- https://doi.org/10.3390/sym14071396