Record link: 
http://hdl.handle.net/20.500.12708/218302
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Title: 
The Hadwiger theorem on convex functions, II: Cauchy–Kubota formulas
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Citation: 
Colesanti, A., Ludwig, M., & Mussnig, F. (2025). The Hadwiger theorem on convex functions, II: Cauchy–Kubota formulas. American Journal of Mathematics, 147(4), 927–955. https://doi.org/10.1353/ajm.2025.a966289
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Publisher DOI: 
10.1353/ajm.2025.a966289
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Colesanti, Andrea 
Ludwig, Monika 
Mussnig, Fabian 
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Organisational Unit: 
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie 
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Journal: 
American Journal of Mathematics 
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ISSN: 
0002-9327
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Date (published): 
Aug-2025
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Number of Pages: 
29
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Publisher: 
JOHNS HOPKINS UNIV PRESS
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Peer reviewed: 
Yes
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Keywords: 
valuation on functions; integral geometry
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Abstract: 
A new version of the Hadwiger theorem on convex functions is established and an explicit representation of functional intrinsic volumes is found using new functional Cauchy–Kubota formulas. In addition, connections between functional intrinsic volumes and their classical counterparts are obtained and non-negative valuations are classified.
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Project title: 
Bewertungen auf konvexen Funktionen: P 34446-N (FWF - Österr. Wissenschaftsfonds) 
Hessische Ungleichungen und Erweiterungen auf Sobolev-Räumen: J 4490 (FWF - Österr. Wissenschaftsfonds) 
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Project (external): 
ERC
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Project ID: 
770127
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Research Areas: 
Fundamental Mathematics Research: 100%
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Science Branch: 
1010 - Mathematik: 100%
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