A capillarity model for soap films

We study a variational model for soap films based on capillarity theory and its relation to minimal surfaces. Here soap films are modeled, not as surfaces, but as regions of small volume satisfying a homotopic spanning condition. The addition of a volume constraint adds a length scale to the Plateau problem, and has the potential to better describe the effect of surface tension on thin films by capturing behaviors related to thickness that are inaccessible by surface models.