DISTANCE FUNCTIONS ON CONVEX BODIES AND SYMPLECTIC TORIC MANIFOLDS

Abstract In this paper we discuss three distance functions on the set of convex bodies. In particular we study the convergence of Delzant polytopes, which are fundamental objects in symplectic toric geometry. By using these observations, we derive some convergence theorems for symplectic toric manifolds with respect to the Gromov–Hausdorff distance.

Authors

Ayato Mitsuishi (ORCID: https://orcid.org/0009-0002-8144-8829)
H. Fujita (ORCID: https://orcid.org/0000-0002-1405-0805)
Yu Kitabeppu (ORCID: https://orcid.org/0000-0002-5043-841X)

Institutions

Japan Women's University (JP)
Fukuoka University (JP)
Kumamoto University (JP)

Publication Details

Journal: Nagoya Mathematical Journal
Published: 2025-04-02
DOI: https://doi.org/10.1017/nmj.2025.13
Primary Topic: Geometric and Algebraic Topology
Type: article
Field-Weighted Citation Impact: 0.00

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article

DISTANCE FUNCTIONS ON CONVEX BODIES AND SYMPLECTIC TORIC MANIFOLDS

Ayato Mitsuishi, H. Fujita, Yu Kitabeppu

Apr 2, 2025

Nagoya Mathematical Journal

Geometric and Algebraic Topology

article

DISTANCE FUNCTIONS ON CONVEX BODIES AND SYMPLECTIC TORIC MANIFOLDS

Ayato Mitsuishi, H. Fujita, Yu Kitabeppu

April 2, 2025article en

Abstract

Abstract In this paper we discuss three distance functions on the set of convex bodies. In particular we study the convergence of Delzant polytopes, which are fundamental objects in symplectic toric geometry. By using these observations, we derive some convergence theorems for symplectic toric manifolds with respect to the Gromov–Hausdorff distance.

Nagoya Mathematical JournalVol. 260

Japan Women's University (JP), Fukuoka University (JP), Kumamoto University (JP)

Openalex Percentile: Top 89%

Geometric and Algebraic Topology

DOI Source OpenAlex

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