Related papers: Overtwisted energy-minimizing curl eigenfields

Consider a knot $K$ in $S^3$ with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still of theoretical and physical interest to understand the…

We consider the nonlinear curl-curl problem $\nabla\times\nabla\times U + V(x) U= \Gamma(x)|U|^{p-1}U$ in $\mathbb{R}^3$ related to the nonlinear Maxwell equations for monochromatic fields. We search for solutions as minimizers (ground…

We give a possible generalization of Lutz twist to all dimensions. This reproves the fact that every contact manifold can be given a non-fillable contact structure and also shows great flexibility in the manifolds that can be realized as…

In this paper, we propose a discrete version of O'Hara's knot energy defined on polygons embedded in the Euclid space. It is shown that values of the discrete energy of polygons inscribing the curve which has bounded O'Hara's energy…

We define \emph{$0$-shifted} and \emph{$+1$-shifted contact structures} on differentiable stacks, thus laying the foundations of \emph{shifted Contact Geometry}. As a side result we show that the kernel of a multiplicative $1$-form on a Lie…

We consider an isoperimetric problem involving the smallest positive and largest negative curl eigenvalues on abstract ambient manifolds, with a focus on the standard model spaces. We in particular show that the corresponding eigenvalues on…

We study some examples of minimal length curves in homogeneous spaces of B(H) under a left action of a unitary group. Recent results relate these curves with the existence of minimal (with respect to a quotient norm) anti-Hermitian…

This presentation reviews recent developments in the understanding of low-energy kaon-nucleon interactions as they relate to the possible existence of antikaon-nuclear quasibound states. A state-of-the-art discussion of low-energy \bar{K}N…

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…

We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to…

We present analysis of a single channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low-energy…

We introduce a generalization of Mobius energy for knots to an energy functional for tubular neighbourhoods of closed inextensible curves. We prove the continuity of the energy and its boundedness for physically admissible tubes without…

We discuss the problem of the optimal design of a micro-tubular fuel cell applying an inverse homogenization technique. Fuel cells are extremely clean and efficient electrochemical power generation devices, made up of a…

We consider a non-local interaction energy over bounded densities of fixed mass $m$. We prove that under certain regularity assumptions on the interaction kernel these energies admit minimizers given by characteristic functions of sets when…

We construct $Q$-curvature operators on $d$-closed $(1,1)$-forms and on $\overline{\partial}_b$-closed $(0,1)$-forms on five-dimensional pseudohermitian manifolds. These closely related operators give rise to a new formula for the scalar…

We prove a compactness theorem for sequences of low-action punctured holomorphic curves of controlled topology, in any dimension, without imposing the typical assumption of uniformly bounded Hofer energy. In the limit, we extract a family…

If a closed 3-manifold M supports a closed, nonsingular, irrational 1-form which linearly deforms into contact forms, then M supports a K-contact form. On the 3-torus, a closed nonsingular 1-form deforms linearly into contact forms if and…

We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total…

The purposes of the present paper are two-fold. Firstly we further develop the interplay between the contact Hamiltonian geometry and the geometric analysis of Hamiltonian-perturbed contact instantons with the Legendrian boundary condition,…

We prove that the minimizer in the N\'ed\'elec polynomial space of some degree p > 0 of a discrete minimization problem performs as well as the continuous minimizer in H(curl), up to a constant that is independent of the polynomial degree…