Conelike soap films spanning tetrahedra

TL;DR

This paper presents the first proven examples of non-flat soap films spanning tetrahedral boundaries, introducing a continuous family of such films with unique geometric properties, including specific edge meeting angles.

Contribution

It provides the first rigorous examples of non-flat soap films spanning tetrahedra, expanding understanding of minimal surface configurations in complex boundary shapes.

Findings

Existence of non-flat soap films spanning tetrahedra

Continuous two-parameter family of such soap films

Some films meet boundary edges at angles greater than 120 degrees

Abstract

In this paper we provide the first examples of non-flat soap films proven to span tetrahedra. These are members of a continuous two parameter family of soap films with tetrahedral boundaries. Of particular interest is a two parameter subfamily where each spanning soap film has the property that two minimal surfaces meet along an edge of the boundary at an angle greater than 120 degrees.