Distance functions on convex bodies and symplectic toric manifolds

TL;DR

This paper explores three distance functions on convex bodies, focusing on Delzant polytopes in symplectic toric geometry, and establishes convergence theorems for symplectic toric manifolds using Gromov-Hausdorff distance.

Contribution

It introduces and analyzes new distance functions on convex bodies and applies these to prove convergence results for symplectic toric manifolds.

Findings

Convergence theorems for symplectic toric manifolds

Analysis of three distance functions on convex bodies

Application of Gromov-Hausdorff distance in symplectic geometry

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.