Energy of tori of revolution

TL;DR

This paper proves that among all tori of revolution, the Clifford torus minimizes the surface energy as defined by Auckly and Sadun, highlighting its optimal geometric property.

Contribution

It establishes the minimal surface energy of the Clifford torus within the class of revolution tori, confirming its special geometric status.

Findings

Clifford torus attains minimum surface energy among revolution tori

Surface energy is explicitly minimized at the Clifford torus

Supports the geometric optimality of the Clifford torus

Abstract

We show that the surface energy introduced by Auckly and Sadun attains the minimum value at the Clifford torus among tori of revolution.