相关论文: The Ginzburg-Landau equation in the Heisenberg gro…
In this paper we study intrinsic regular submanifolds of $\mathbb{H}^n$, of low co-dimension in relation with the regularity of their intrinsic parametrization. We extend some results proved for one co-dimensional $\mathbb{H}$-regular…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note is the introduction of a concept of mildly degenerate…
A set of locally finite perimeter $E \subset \mathbb{R}^{n}$ is called an anisotropic minimal surface in an open set $A$ if $\Phi(E;A) \le \Phi(F;A)$ for some surface energy $\Phi(E;A) = \int_{\partial^{*}E \cap A} \| \nu_{E}\| d…
In this work, based on some mathematical results obtained by Yamabe, Osgood, Phillips and Sarnak, we demonstrate that in dimensions three and higher the famous Ginzburg-Landau equations used in theory of phase transitions can be obtained…
This paper considers minimizers of the Ginzburg-Landau energy functional in special multiscale spaces that are based on finite elements. The spaces are constructed by localized orthogonal decomposition techniques and their usage for solving…
We study almost-minimizers of anisotropic surface energies defined by a H\"older continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove almost-minimizers…
Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional integer Heisenberg group. For example any finite index subgroup of SL(3,Z) is such a group. The main result of this paper is that every action of…
We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold…
We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of…
Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space $H^1$ over finite-dimensional real space generalized to the case of locally compact groups that are spaces of homogeneous type. Special cases…
We investigate, on a bounded domain $\Omega$ of $\R^2$ with fixed $S^1$-valued boundary condition $g$ of degree $d>0$, the asymptotic behaviour of solutions $u_{\varepsilon,\delta}$ of a class of Ginzburg-Landau equations driven by two…
In this paper, we study the structure of the singular set for a $C^{1}$ smooth surface in the $3$-dimensional Heisenberg group $\boldsymbol{H}_{1}$. We discover a Codazzi-like equation for the $p$-area element along the characteristic…
We construct local minimizers to the Ginzburg-Landau functional of superconductivity whose number of vortices N is prescribed and blows up as the parameter epsilon, inverse of the Ginzburg-Landau parameter kappa, tends to zero. We treat the…
It is a well known fact that the geometry of a superconducting sample influences the distribution of the surface superconductivity for strong applied magnetic fields. For instance, the presence of corners induces geometric terms described…
We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group.…
The perennial formalism is applied to the real, massive Klein-Gordon field on a globally-hyperbolic background space-time with compact Cauchy hypersurfaces. The parametrized form of this system is taken over from the accompanying paper. Two…
It is well-known that under suitable hypotheses, for a sequence of solutions of the (simplified) Ginzburg-Landau equations $-\Delta u_\varepsilon +\varepsilon^{-2}(|u_\varepsilon|^2-1)u_\varepsilon = 0$, the energy and vorticity concentrate…
In this paper, we are interested in the construction of quasiconformal mappings between domains of the Heisenberg group H that minimise a mean distortion functional. We propose to construct such mappings by considering a corresponding…
We establish quantitative properties of minimizers and stable sets for nonlocal interaction functionals, including the $s$-fractional perimeter as a particular case. On the one hand, we establish universal $BV$-estimates in every dimension…