Related papers: Minimal surfaces bounded by elastic lines
Assume you are given a finite configuration $\Gamma$ of disjoint rectifiable Jordan curves in $\mathbb{R}^n$. The Plateau-Douglas problem asks whether there exists a minimizer of area among all compact surfaces of genus at most $p$ which…
The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current day efforts to…
In recent years, there has been a considerable interest in the mechanics of soft objects meeting fluid interfaces (elasto-capillary interactions). In this work we experimentally examine the case of a fluid resting on a thin film of rigid…
We prove some non-existence results for the asymptotic Plateau problem of minimal and area minimizing surfaces in the homogeneous space ${\widetilde{\mathrm{SL}}_2(\mathbb{R})}$ with isometry group of dimension 4, in terms of their…
Motivated by a problem originating in the study of defect structures in nematic liquid crystals, we describe and study a numerical algorithm for the resolution of a Plateau-like problem. The energy contains the area of a two-dimensional…
Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean…
Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating non-linear elasticity using geometric invariant quantities. Solutions are generally…
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.…
In this paper, we consider the classical variational problem in the Galilean space. we develop the Euler-Lagrange equations for a elastic line on an oriented surface in the Galilean 3-dimensional space $G_3$. Using the varia- tion method,…
We study the wetting of a thin elastic filament floating on a fluid surface by a droplet of another, immiscible fluid. This quasi-2D experimental system is the lower-dimensional counterpart of the wetting and wrapping of a droplet by an…
In this paper we give a geometric argument for bounding the diameter of a connected compact surface (with boundary) of arbitrary codimension in Euclidean space in terms of Topping's diameter bound for closed surfaces (without boundary). The…
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,…
We study generalized minimizers in the soap film capillarity model introduced in [arXiv:1807.05200,arXiv:1907.00551]. Collapsed regions of generalized minimizers are shown to be smooth outside of dimensionally small singular sets, which are…
Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value $F_\ast>0$. Here, we extend this classical, planar instability to the…
We consider minimal hypersurfaces inside the unit ball whose boundary on the sphere is a small perturbation of the link of a minimizing quadratic cone. We show that such minimal surfaces are uniquely determined by their boundary condition.…
Enneper's wire, the image of the circle of radius $R$ under Enneper's surface, bounds exactly three minimal surfaces for $R$ between 1 and $\sqrt 3$, and these three surfaces depend continuously on $R$. The other two surfaces (besides…
Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the…
It is well known that an elastic sheet loaded in tension will wrinkle and that the length scale of the wrinkles tends to zero with vanishing thickness of the sheet [Cerda and Mahadevan, Phys. Rev. Lett. 90, 074302 (2003)]. We give the first…
We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…