HIGHER RANK INNER PRODUCTS, VORONOI TILINGS AND METRIC DEGENERATIONS OF TORI

Omid Amini; Noema Nicolussi

doi:10.5802/ahl.257

HIGHER RANK INNER PRODUCTS, VORONOI TILINGS AND METRIC DEGENERATIONS OF TORI

Titre traduit de la contribution: PRODUITS SCALAIRES MULTI-ÉCHELLES, DIAGRAMMES DE VORONOI ET DÉGÉNÉRESCENCES MÉTRIQUES DE TORES

Omid Amini
, Noema Nicolussi

Laboratoire de Mathématiques d'Orsay
Department of Mathematics
University of Innsbruck

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

Titre traduit de la contribution	PRODUITS SCALAIRES MULTI-ÉCHELLES, DIAGRAMMES DE VORONOI ET DÉGÉNÉRESCENCES MÉTRIQUES DE TORES
langue originale	Anglais
Pages (de - à)	1109-1188
Nombre de pages	80
journal	Annales Henri Lebesgue
Volume	8
Les DOIs	https://doi.org/10.5802/ahl.257
état	Publié - 1 janv. 2025
Modification externe	Oui

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10.5802/ahl.257

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title = "HIGHER RANK INNER PRODUCTS, VORONOI TILINGS AND METRIC DEGENERATIONS OF TORI",

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.",

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

author = "Omid Amini and Noema Nicolussi",

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AU - Nicolussi, Noema

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AB - 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.

KW - Voronoi tilings

KW - asymptotic polyhedral geometry

KW - higher rank inner products

KW - higher rank tropical geometry

KW - metric collapse

KW - multi-scale geometry

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U2 - 10.5802/ahl.257

DO - 10.5802/ahl.257

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JO - Annales Henri Lebesgue

JF - Annales Henri Lebesgue

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HIGHER RANK INNER PRODUCTS, VORONOI TILINGS AND METRIC DEGENERATIONS OF TORI

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