# A note on "The Cartan-Hadamard conjecture and the Little Prince"

## TL;DR

This paper offers straightforward proofs of key lemmas from a work on the Cartan-Hadamard conjecture, facilitating the derivation of new isoperimetric inequalities without complex algebraic computations.

## Contribution

It provides elementary, Sage-free proofs of lemmas crucial for establishing novel isoperimetric inequalities related to the Cartan-Hadamard conjecture.

## Key findings

- Elementary proofs of Lemmas 7.1 and 7.4
- Simplification of proof techniques for isoperimetric inequalities
- Elimination of reliance on symbolic algebra software

## Abstract

We provide elementary proofs of Lemmas 7.1 and 7.4 appearing in "The Cartan-Hadamard conjecture and the Little Prince", by B. Kloeckner and G. Kuperberg. The Lemmas play an important role in the derivation of novel isoperimetric inequalities. The original proofs relied on Sage, a symbolic algebra package, to factor certain algebraic varieties into irreducible components.