Abstract
This paper attempts to look at the interconnections existing between metrics, convexity, and integral geometry from the point of view of combinatorial integral geometry. Along with general expository material, some new concepts and results are presented, in particular the sin2-representations of breadth functions, translative versions of mean curvature integral, and the notion of 2-zonoids. The main aim is to apply these new ideas for a better understanding of the nature of zonoids.
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Ambartzumian, R.V. Combinatorial integral geometry, metrics, and zonoids. Acta Applicandae Mathematicae 9, 3–27 (1987). https://doi.org/10.1007/BF00580819
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DOI: https://doi.org/10.1007/BF00580819