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DISTANCE FUNCTIONS ON CONVEX BODIES AND SYMPLECTIC TORIC MANIFOLDS

Published online by Cambridge University Press:  02 April 2025

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 [email protected]
AYATO MITSUISHI
Affiliation:
Faculty of Science Fukuoka University Jonan Ward Fukuoka Japan [email protected]

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.

Type
Article
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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