SL(2) intertwining Minkowski valuations in the plane

SL(2) intertwining Minkowski valuations in the plane

The polygon valued Minkowski valuations in R2 intertwining with the special linear group are completely classified in this paper without any additional assumptions. Our results characterize projection bodies and difference bodies in R2. There are also some SL(2) intertwining Minkowski valuations tha...

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Veröffentlicht in:Advances in applied mathematics 2021-09, Vol.130, p.102231, Article 102231
Hauptverfasser: Leng, Gangsong, Ma, Liangying
Format: Artikel
Sprache:eng
Schlagworte:
2-dimensional space
Blaschke valuation
Difference body
Mathematics
Mathematics, Applied
Minkowski valuation
Physical Sciences
Polygon
Projection body
Science & Technology
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Zusammenfassung:The polygon valued Minkowski valuations in R2 intertwining with the special linear group are completely classified in this paper without any additional assumptions. Our results characterize projection bodies and difference bodies in R2. There are also some SL(2) intertwining Minkowski valuations that can only be defined in R2. It somehow suggests why such classification problems are more complicated than higher dimensional spaces.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2021.102231