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Plateau's soap film problem is to find a surface of least area spanning a given boundary. We begin with a compact orientable $(n-2)$-dimensional submanifold $M$ of $\R^n$. If $M$ is connected, we say a compact set $X$ "spans" $M$ if $X$…
In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examples of soap films compatible with the covering space method:…
The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the…
By employing the method of moving planes in a novel way we extend some classical symmetry and rigidity results for smooth minimal surfaces to surfaces that have singularities of the sort typically observed in soap films.
The present study aims to investigate the motion of buoyant rings in vertical soap films. Thickness differences and related bi-dimensional densities are considered as the motor leading to bi-dimensional buoyancy. We show how this effect can…
The interaction that occurs between a light solid object and a horizontal soap film of a bamboo foam contained in a cylindrical tube is simulated in 3D. We vary the shape of the falling object from a sphere to a cube by changing a single…
Soap bubbles are thin liquid films enclosing a fixed volume of air. Since the surface tension is typically assumed to be the only responsible for conforming the soap bubble shape, the realized bubble surfaces are always minimal area ones.…
Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we…
Surface bubbles are present in many industrial processes and in nature, as well as in CO$_2$ beverage. They have motivated many theoretical, numerical and experimental works. This paper presents the current knowledge on the physics of…
Very simple experiments based on an analogy between two theories (gravitation and capillarity) allowed us to construct a two dimension space toy-universe composed of the surface of a three-dimensional water tank with floating soap bubbles…
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…
Plateau's problem is to show the existence of an area minimizing surface with a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by Plateau showed that an area minimizing surface can be obtained in the form of a…
We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some…
Cox & Jones recently devised and studied an interesting variant of the classical Plateau problem, a variant in which a helical soap film is confined to a cylindrical tube with circular cross-section. Through experiments, numerics, and some…
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…
We investigate the sliding dynamics of a millimeter-sized particle trapped in a horizontal soap film. Once released, the particle moves toward the center of the film in damped oscillations. We study experimentally and model the forces…
We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance lambda(t), due to the formation of a…
The solution to the Euler-Lagrange equation is an extremal functional.To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using soap film to form a catenoid. A…
Surface tension profiles in vertical soap films are experimentally investigated. Measurements are performed introducing deformable elastic objets in the films. The shape adopted by those objects set in the film can be related to the surface…
Soap bubbles form when blowing air through a suspended thin film of soapy water and this phenomenon entertains children and adults alike. The formation of soap bubbles from thin films is accompanied by topological transitions, and thus the…