Should we solve Plateau's problem again?

TL;DR

This paper reviews classical solutions to Plateau's problem, explores alternative models for soap films, and discusses open questions, with a focus on a specific model involving deformations and sliding boundary conditions.

Contribution

It introduces a detailed discussion of alternative soap film models and examines open questions, especially concerning deformations and sliding boundary conditions.

Findings

Classical solutions of Plateau's problem are summarized.

Alternative models for soap films are proposed and analyzed.

Open questions regarding deformations and boundary conditions are identified.

Abstract

After a short description of various classical solutions of Plateau's problem, we discuss other ways to model soap films, and some of the related questions that are left open. A little more attention is payed to a more specific model, with deformations and sliding boundary conditions.