Higher rank inner products, Voronoi tilings and metric degenerations of tori
Annales Henri Lebesgue, Volume 8 (2025), pp. 1109-1188

Metadata

Keywords higher rank inner products ,  multi-scale geometry ,  metric collapse ,  asymptotic polyhedral geometry ,  higher rank tropical geometry ,  Voronoi tilings

Abstract

We introduce a multi-scale generalization of the notion of scalar product on real and complex vector spaces and study the corresponding Voronoi tilings. This framework allows to analyze limiting metric structures involving several levels of convergence. In particular, we describe metric degenerations of polarized tori and Hausdorff limits of Voronoi tilings.


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