# Symmetric Mahler's conjecture for the volume product in the three dimensional case

## TL;DR

This paper proves Mahler's conjecture for the volume product of centrally symmetric convex bodies specifically in three dimensions and identifies the conditions for equality.

## Contribution

It provides the first proof of Mahler's conjecture in three dimensions and characterizes the equality cases for symmetric convex bodies.

## Key findings

- Mahler's conjecture holds in 3D for symmetric convex bodies.
- The equality condition for the volume product is characterized.
- The proof confirms the conjecture's validity in the three-dimensional case.

## Abstract

In this paper, we prove Mahler's conjecture concerning the volume product of centrally symmetric convex bodies in $\mathbb{R}^n$ in the case where $n=3$. Furthermore, we determine the equality condition.