Additive Kinematic Formulas for Functional Minkowski Vectors
Mohamed A. Mouamine
TL;DR
This paper develops an additive kinematic formula for functional Minkowski vectors, utilizing mixed Monge-Ampère measures, marking the first integral geometric application of these recently introduced vector-valued valuations on convex functions.
Contribution
It introduces a novel additive kinematic formula for functional Minkowski vectors based on mixed Monge-Ampère measures, expanding integral geometry into convex functions.
Findings
Established an additive kinematic formula for functional Minkowski vectors.
Connected the formula to mixed Monge-Ampère measures.
First application of these valuations in integral geometry.
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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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Algebraic and Geometric Analysis · Advanced Differential Geometry Research