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DISTANCE FUNCTIONS ON CONVEX BODIES AND SYMPLECTIC TORIC MANIFOLDS

Part of: Symplectic geometry, contact geometry Polytopes and polyhedra Global differential geometry

Published online by Cambridge University Press:  02 April 2025

HAJIME FUJITA Open the ORCID record for HAJIME FUJITA [Opens in a new window] ,
YU KITABEPPU Open the ORCID record for YU KITABEPPU [Opens in a new window]  and
AYATO MITSUISHI Open the ORCID record for AYATO MITSUISHI [Opens in a new window]
HAJIME FUJITA*
Affiliation:
Faculty of Science Japan Women’s University Bunkyo City Tokyo Japan
YU KITABEPPU
Affiliation:
Faculty of Advanced Science and Technology Kumamoto University Chuo Ward Kumamoto Japan ybeppu@kumamoto-u.ac.jp
AYATO MITSUISHI
Affiliation:
Faculty of Science Fukuoka University Jonan Ward Fukuoka Japan mitsuishi@fukuoka-u.ac.jp
*
fujitah@fc.jwu.ac.jp
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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.

Keywords

Delzant polytopesymplectic toric manifoldGromov–Hausdorff convergence

MSC classification

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 53D20: Momentum maps; symplectic reduction 52B12: Special polytopes (linear programming, centrally symmetric, etc.)

Information

Type
Article
Information
Nagoya Mathematical Journal , Volume 260 , December 2025 , pp. 625 - 647
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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