Related papers: Stationary Surfaces with Boundaries
In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. These…
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper…
This is the first comprehensive introduction to the authors' recent attempts toward a better understanding of the global concepts behind spinor representations of surfaces in 3-space. The important new aspect is a quaternionic-valued…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of…
A four dimensional conformally invariant energy is studied. This energy generalises the well known two-dimensional Willmore energy. Although not positive definite, it includes minimal hypersurfaces as critical points. We compute its first…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
In this paper, we systemically study the conformation characters of rotational symmetric gel sheets with free boundary and investigate the role of boundary on the equilibrium conformation. In gel sheet the boundary provides a residual…
We develop and analyze a variational model for multi-ply (i.e., multi-layered) paperboard. The model consists of a number of elastic sheets of a given thickness, which -- at the expense of an energy per unit area -- may delaminate. By…
We investigate the energy landscape of two- and three-dimensional XY models with nearest-neighbor interactions by analytically constructing several classes of stationary points of the Hamiltonian. These classes are analyzed, in particular…
Force fluctuations in granular materials are investigated. A continuum equation is derived starting from a discrete model proposed in the literature. The influence of boundary conditions is investigated. For periodic boundary conditions the…
In this paper we study a constrained minimization problem for the Willmore functional. For prescribed surface area we consider smooth embeddings of the sphere into the unit ball. We evaluate the dependence of the the minimal Willmore energy…
The problem of disturbed flow in the laminar boundary layer is investigated when a heating element is located on the surface of the body. The flow is supposed to be laminar one. It is shown that the problem may be solved in terms of free…
Grain boundaries affect properties of polycrystalline materials. The influence of a boundary is largely determined by its energy. Grain boundary energy is often portrayed as a function of macroscopic boundary parameters representing grain…
We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in H3, particularly those related to assumptions on boundedness or smallness of a certain weighted version of the Willmore energy. We…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
Following arXiv:1501.03019 [hep-th], we study de Sitter space and spherical subregions on a constant boundary Euclidean time slice of the future boundary in the Poincare slicing. We show that as in that case, complex extremal surfaces exist…
We study the dynamics of the boundary dilaton gravity coupled to N massles scalars. We rederive the boundary conditions of [1] and [3] in a way which makes the requirement of reparametrization invariance and role of conformal anomaly…
The Willmore energy of a closed surface in R^n is the integral of its squared mean curvature, and is invariant uner M\"obius transformations of R^n. We show that any torus in R^3 with energy at most $8 \pi-delta$ has a representative under…