Related papers: Isotropic realizability of current fields in R^3

In this paper we study the isotropic realizability of a given regular gradient field $\nabla u$ as an electric field, namely when $\nabla u$ is solution of the equation $\div\left(\si\nabla u\right)=0$ for some isotropic conductivity…

The paper is devoted to the isotropic realizability of a regular gradient field u or a more general vector field b, namely the existence of a continuous positive function $\sigma$ such that $\sigma$b is divergence free in R d or in an open…

In this paper we study the isotropic realizability of a given non smooth gradient field $\nabla u$ defined in $\mathbb{R}^d$, namely when one can reconstruct an isotropic conductivity $\sigma>0$ such that $\sigma\nabla u$ is divergence free…

In the paper we study the problem of the isotropic realizability in R^2 of a regular strain field e(U)=1/2(DU+DU^T) for the incompressible Stokes equation, namely the existence of a positive viscosity mu\textgreater{}0 solving the Stokes…

Under an assumption of normal genericity, we show that a stable J-holomorphic curve has, in the space of homologous curves of the same genus, a locally Euclidean neighbourhood of the expected dimension given by Riemann-Roch. In dimension 4,…

In this article, by following the method in \cite{PT}, combining Willmore energy with isoperimetric inequalities, we construct two examples of singularities under mean curvature flow in $\mathbb{H}^3$. More precisely, there exists a torus,…

Lumley [Lumley J.L.: Adv. Appl. Mech. 18 (1978) 123--176] provided a geometrical proof that any Reynolds-stress tensor $\overline{u_i'u_j'}$ (indeed any tensor whose eigenvalues are invariably nonnegative) should remain inside the so-called…

We consider the problem of isotropic effective conductivity $\sigma_e(\sigma_1,\ldots,\sigma_n)$ in two-dimensional three- and four-phase symmetric composites with a partial isotropic conductivity $\sigma_j$ of the $j$-th phase. The upper…

This paper presents the reachability analysis of curves in $\mathbb{R}^3$ with a prescribed curvature bound. Based on Pontryagin Maximum Principle, we leverage the existing knowledge on the structure of solutions to minimum-time problems,…

The effective dc-conductivity problem of isotropic, two-dimensional (2D), three-component, symmetric, regular composites is considered. A simple cubic equation with one free parameter for $\sigma_{e}(\sigma_1,\sigma_2,\sigma_3)$ is…

The RG flow equation of various transport quantities are studied in arbitrary spacetime dimensions, in the fixed as well as fluctuating background geometry both for the Maxwellian and DBI type of actions. The regularity condition on the…

Given a contact 3-manifold we consider the problem of when a given function can be realized as the Ricci curvature of a Reeb vector field for the contact structure. We will use topological tools to show that every admissible function can be…

This article addresses the solvability of the multi-dimensional divergence-curl problem with a no-slip boundary condition. A solvability criterion is derived as an orthogonality condition of the vorticity function to pseudo-harmonic fields.…

An electrical potential U on bordered surface X (in Euclidien three-dimensional space) with isotropic conductivity function sigma>0 satisfies equation d(sigma d^cU)=0, where d^c is real operator associated with complex (conforme) structure…

Let $\mathbb{Q}_3$ be the complex 3-quadric endowed with its standard complex conformal structure. We study the complex conformal geometry of isotropic curves in $\mathbb{Q}_3$. By an isotropic curve we mean a nonconstant holomorphic map…

The geodesic flow of a Riemannian metric on a compact manifold $Q$ is said to be toric integrable if it is completely integrable and the first integrals of motion generate a homogeneous torus action on the punctured cotangent bundle…

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds $M^3$. Given a conformal vector field $V\in\mathfrak{X}(M^3)$, a conformal trajectory of $V$ is a regular curve $\gamma$ in $M^3$ satisfying…

We study the fillability (or embeddability) of 3-dimensional $CR$ structures under the geometric flows. Suppose we can solve a certain second order equation for the geometric quantity associated to the flow. Then we prove that if the…

We give a numerical condition for right-handedness of a dynamically convex Reeb flow on the $3$-sphere. Our condition is stated in terms of an asymptotic ratio between the amount of rotation of the linearised flow and the linking number of…

In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive…