# Appendix to V. Mathai and J. Rosenberg's paper "A noncommutative sigma-model"

## TL;DR

This paper proves a conjecture regarding the minimal energy of unitaries in noncommutative tori and establishes lower bounds for energies of unital *-endomorphisms, advancing understanding in noncommutative geometry.

## Contribution

It confirms Rosenberg's conjecture on minimal energies and provides new lower bounds for energies of *-endomorphisms in noncommutative tori.

## Key findings

- Proved Rosenberg's conjecture on minimal energy values.
- Established lower bounds for energies of unital *-endomorphisms.
- Enhanced understanding of energy minimization in noncommutative tori.

## Abstract

We prove a conjecture of Rosenberg about the minimal value for energies of untaries in the two-dimensional noncommutative tori and answer a question of his about lower bounds for energies of unital *-endomorphisms of the two-dimensional noncommutative tori.