相关论文: Geometric invariance from outer surfaces: Laplace-…
We consider a magnetic Laplacian on a geometrically finite hyperbolic surface, when the corresponding magnetic field is infinite at the boundary at infinity. We prove that the counting function of the eigenvalues has a particular asymptotic…
The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the…
The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplace's equation that is accessible for an…
We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…
Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework…
We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…
Let X be a manifold equipped with a complete Riemannian metric of constant negative curvature and finite volume. We demonstrate the finiteness of the collection of totally geodesic immersed hypersurfaces in X that lie in the zero-level set…
Is field space infinite? If not, it either loops back on itself or ends altogether. Periodic boundary conditions are of course familiar, but field space endpoints--which appear in real-world systems--are far less explored. In this paper we…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
Consider a smooth closed surface $M$ of fixed genus $\geqslant 2$ with a hyperbolic metric $\sigma$ of total area $A$. In this article, we study the behavior of geometric and dynamical characteristics (e.g., diameter, Laplace spectrum,…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…
We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate asymptotics of the low-lying eigenvalues in the weak…
On a closed hyperbolic surface, we investigate semiclassical defect measures associated with the magnetic Laplacian in the presence of a constant magnetic field. Depending on the energy level where the eigenfunctions concentrate, three…
We evaluate the conditions for surface stability of a layered magnetoelastic half-space subjected to large deformations and a magnetic field. After reviewing the fundamental measures of deformation and summarizing the magnetostatic…
On gas giant planets the speed of sound is isotropic and goes to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal blow-up near the boundary. The blow-up is tamer than in…
The influence of a magnetic field on superconductivity is usually described either phenomenologically, using Ginzburg-Landau theory, or semiclassically using Gor'kov theory. In this article we discuss the influence of magnetic fields on the…
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…
We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…
The noncommutativity concept has wide range of applications in physical and mathematical theories. Noncommutativity in the position-time coordinates concerns the microscale structure of space-time. the noncommutativity is an intrinsic…