Breaking glass optimally and Minkowski's problem for polytopes (Jian-Guo Liu, Duke University)

Séminaire « Analyse numérique et équations aux dérivées partielles »
Salle de séminaire M3

Motivated by a study of least-action incompressible flows, we study all the ways that a given convex body in Euclidean space can break into countably many pieces that move away from each other rigidly at constant velocity, following geodesic motions in the sense of optimal transport theory. These we classify in terms of a countable version of Minkowski's geometric problem of determining convex polytopes by their face areas and normals. Illustrations involve various intriguing examples both fractal and paradoxical, including Apollonian packings and other types of full packings by smooth balls.

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