Knörr, J. (2025). Singular Valuations and the Hadwiger Theorem on Convex Functions. Journal of Geometric Analysis, 35(11), Article 336. https://doi.org/10.1007/s12220-025-02170-6
We give a classification of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions, originally established by Colesanti, Ludwig and Mussnig. We also give a description of the construction of the functional intrinsic volumes using integration over the differential cycle and provide a new representation of these functionals as principal value integrals with respect to the Hessian measures.
