The Hadwiger Theorem on Convex Functions, I
Abstract A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb{R}}^{n}$ is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.
Authors
- Monika Ludwig (ORCID: https://orcid.org/0000-0002-7389-6720)
- Fabian Mussnig (ORCID: https://orcid.org/0000-0003-2012-1590)
- Andrea Colesanti (ORCID: https://orcid.org/0000-0003-1154-7952)
Institutions
- TU Wien (AT)
- Tel Aviv University (IL)
- University of Florence (IT)
Publication Details
- Journal
- Geometric and Functional Analysis
- Published
- 2024-10-16
- DOI
- https://doi.org/10.1007/s00039-024-00693-8
- Citations
- 13
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 9.75