# The isoperimetric problem for Lens spaces

## TL;DR

This paper solves the isoperimetric problem in Lens spaces with large fundamental groups, identifying the isoperimetric surfaces as geodesic spheres or tori of revolution, and connects special cases to the Willmore conjecture proof.

## Contribution

It provides a complete solution for large fundamental group Lens spaces and links specific cases to the Willmore conjecture, advancing geometric analysis in these spaces.

## Key findings

- Isoperimetric surfaces are geodesic spheres or tori of revolution.
- Solution applies to Lens spaces with large fundamental groups.
- Special cases relate to the proof of the Willmore conjecture.

## Abstract

We solve the isoperimetric problem in the Lens spaces with large fundamental group. Namely, we prove that the isoperimetric surfaces are geodesic spheres or tori of revolution about geodesics. We also show that the isoperimetric problem in L(3,1) and L(3,2) follows from the proof of the Willmore conjecture by Marques and Neves.