# Extremal convex bodies for affine measures of symmetry

## TL;DR

This paper investigates measures of symmetry for convex bodies using distances between centroids and special ellipsoid centers, providing precise bounds and advancing understanding of geometric symmetry measures.

## Contribution

It introduces new bounds for symmetry measures based on centroid and ellipsoid centers, improving accuracy in geometric symmetry analysis.

## Key findings

- Derived upper bounds for symmetry measures are proven to be accurate.
- The measures based on centroid and ellipsoid centers effectively quantify convex body symmetry.
- The results enhance the theoretical understanding of symmetry in convex geometry.

## Abstract

This paper is devoted to measures of symmetry based on distance between centroid and one of the centers of John and Lowner ellipsoid. The author proves the accuracy of the derived upper bounds for the considered measures of symmetry.