# Plateau's problem as a singular limit of capillarity problems

## TL;DR

This paper models soap films as small-volume regions within a capillarity framework, introducing a length scale to Plateau's problem and providing a new energy-based approach to understanding minimal surfaces.

## Contribution

It presents a novel approximation of area-minimizing hypersurfaces via capillarity problems with homotopic spanning conditions, revealing new physical insights.

## Key findings

- Length scale introduced in classical Plateau's problem.
- Energy-based selection principle for soap films.
- Connections between capillarity models and minimal surfaces.

## Abstract

Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection principle for Plateau's problem, points at physical features of soap films that are unaccessible by simply looking at minimal surfaces, and opens several challenging questions.