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Titlebook: Analytic Aspects of Convexity; Gabriele Bianchi,Andrea Colesanti,Paolo Gronchi Book 2018 Springer International Publishing AG 2018 Convex

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Dual Curvature Measures in Hermitian Integral Geometry,ture measures. Building on the recent results from integral geometry in complex space forms, we describe this algebra structure explicitly as a polynomial algebra. This is a short way to encode all local kinematic formulas. We then characterize the invariant valuations on complex space forms leaving
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Crofton Formulae for Tensorial Curvature Measures: The General Case,r generalizations some of which also have continuous extensions to arbitrary convex bodies. In a previous work, we obtained kinematic formulae for all (generalized) tensorial curvature measures. As a consequence of these results, we now derive a complete system of Crofton formulae for such (generali
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Discrete Centro-Affine Curvature for Convex Polygons,pectively, for polygons. These concepts of affine length are shown to be similar to their counterparts defined for smooth convex bodies in that they satisfy analogous affine isoperimetric type inequalities.
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