# Cosine formula for generalized O'Hara's energies

## TL;DR

This paper extends the cosine formula to generalized O'Hara energies, providing conditions for energy minimization and insights into their deviation from M"obius invariance.

## Contribution

It introduces a generalized cosine formula for O'Hara energies and analyzes their minimization and invariance properties.

## Key findings

- Derived a cosine formula for generalized O'Hara energies
- Identified conditions for circle minimizers under length constraints
- Quantified deviation from M"obius invariance

## Abstract

In this short article, we extend the cosine formula for the M\"{o}bius energy to generalized O'Hara energies. The newly derived formula gives us a condition for which the right circle minimizes the energy under the length-constraint. Furthermore, it shows us how far the energy is from the M\"{o}bius invariant property.