Related papers: Membrane geometry with auxiliary variables and qua…

Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…

If a catenoid is inverted in any interior point, a deflated compact geometry is obtained which touches at two points (its poles). The catenoid is a minimal surface and, as such, is an equilibrium shape of a symmetric fluid membrane. The…

Given a triangulation of a closed orientable surface, we place single-mode resonators or single-orbital artificial atoms at its vertices, edges and facets, and we devise near-neighbor hopping terms derived from the boundary and Poincar\'e…

In this paper we show that in addition to the known minimal surfaces which appear in the literature for computing the entanglement entropy there are other minimal surfaces with non-zero extrinsic curvature. We use the approach of…

Let $M$ be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into $M$ is bounded by a multiple of its extrinsic curvature energy, i.e. by a…

The assembly of banana-shaped rodlike proteins on membranes, and the associated membrane shape transformations, are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two…

Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…

We study the deformation of a liquid interface with arbitrary principal curvatures by a flat circular sheet. Working first at small slopes, we determine the shape of the sheet analytically in the membrane limit, where the sheet is…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key…

Investigating the geometric effects resulting from the detailed behaviors of the confining potential, we consider square and circular confinements to constrain a particle to a space curve. We find a torsion-induced geometric potential and a…

Hamiltonian formulations of M-branes moving in curved backgrounds are given.

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…

This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…

The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposition of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is…

We extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a 2-form on submanifolds associated with the nontrivial ambient…

We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized…

This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite…

How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially relate the constraint structure…