Additive Kinematic Formulas for Functional Minkowski Vectors
Metric Geometry
2026-05-20 v2 Functional Analysis
Abstract
We establish an additive kinematic formula for the functional Minkowski vectors using mixed Monge-Amp\`ere measures. These vectors, recently introduced and characterized by the author and F. Mussnig, form a natural family of vector-valued valuations on the space of convex functions. This result represents the first integral geometric application of this characterization.
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Cite
@article{arxiv.2508.07984,
title = {Additive Kinematic Formulas for Functional Minkowski Vectors},
author = {Mohamed A. Mouamine},
journal= {arXiv preprint arXiv:2508.07984},
year = {2026}
}
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