Related papers: Soap films: from the Plateau problem to deformable…
We study the Plateau problem with a lower dimensional obstacle in $\mathbb{R}^n$. Intuitively, in $\mathbb{R}^3$ this corresponds to a soap film (spanning a given contour) that is pushed from below by a "vertical" 2D half-space (or some…
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…
Filtration of real gases described by Peng-Robinson equations of state in 3-dimensional space is studied. Thermodynamic states are considered as either Legendrian submanifolds in contact space, or Lagrangian submanifolds in symplectic…
A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place…
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.
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
In the past few years, the research on sober spaces and well-filtered spaces has got some breakthrough progress. In this paper, we shall present a brief summarising survey on some of such development. Furthermore, we shall pose and…
In this paper we consider the heat flow associated to the classical Plateau problem for surfaces of prescribed mean curvature. We show that an isoperimetric condition on H ensures the existence of a global weak solution. Moreover, we…
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…
Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…
The collapse of a catenoidal soap film when the rings supporting it are moved beyond a critical separation is a classic problem in interface motion in which there is a balance between surface tension and the inertia of the surrounding air,…
A number of unsolved problems and open questions about the nature and the properties of supernovae are identified and briefly discussed. Some suggestions and directions toward possible solutions are also considered.
We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the…
We present a novel and comprehensive approach to the study of the parametric Plateau problem for locally strictly convex (LSC) hypersurfaces of prescribed curvature for general convex curvature functions inside general Riemannian manifolds.…
A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric…
By integrating the Young-Laplace equation, including the effects of gravity, we have calculated the equilibrium shape of the two-dimensional Plateau borders along which a vertical soap film contacts two flat, horizontal solid substrates of…
Real foams can be viewed as a geometrically well-organized dispersion of more or less spherical bubbles in a liquid. When the foam is so drained that the liquid content significantly decreases, the bubbles become polyhedral-like and the…
A metallic film of arbitrary thickness is considered. We show that the problem of description of surface plasma oscillations (surface plasmons) with reflection boundary conditions allows analytic solution. Besides, this problem allows…
Using the Perron method, we prove the existence of hypersurfaces of prescribed special Lagrangian curvature with prescribed boundary inside complete Riemannian manifolds of non-positive curvature.