Related papers: Boundary behaviour of harmonic functions on hyperb…
We extend ferromagnetic resonance (FMR) modulation theory to describe systems in which bulk and boundary states of topological materials coexist, with both appearing at the same energy. As an application of the formulation, we investigate…
After introducing the different boundary geometries of rank one symmetric spaces, we state and prove Fried's theorem in the general setting of all those geometries: a closed manifold with a similarity structure is either complete or the…
We show that there are harmonic functions on a ball ${\mathbb{B}_n}$ of $\mathbb{R}^n$, $n\ge 2$, that are continuous up to the boundary (and even H\"older continuous) but not in the Sobolev space $H^s(\mathbb{B}_n)$ for any $s$…
We study the map from conductances to edge energies for harmonic functions on finite graphs with Dirichlet boundary conditions. We prove that for any compatible acyclic orientation and choice of energies there is a unique choice of…
In this paper, we define natural capacities using a relative volume of graphs over manifolds, which can be characterized by solutions of bounded variation to Dirichlet problems of minimal hypersurface equation. Using the capacities, we…
Given two Riemannian manifolds $M$ and $N\subset\mathbb{R}^L$, we consider the energy concentration phenomena of the penalized energy functional $$E_{\epsilon}(u)=\int_M\frac{\vert\nabla u\vert^2}{2}+\frac{F(u)}{\epsilon^2},u\in…
We prove existence and uniqueness of a solution of the Dirichlet problem for separately $(\alpha, \beta)$ - harmonic functions on the unit polydisc $\mathbb D^n$ with boundary data in $C(\mathbb T^n)$ using $(\alpha, \beta)$ - Poisson…
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic…
In this paper, we study the compactness of a boundary value problem for hyperkaehler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkaehler…
Energy-momentum (and angular momentum) for the Metric-Affine Gravity theory is considered from a Hamiltonian perspective (linked with the Noether approach). The important roles of the Hamiltonian boundary term and the many choices involved…
In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be…
As a consequence of a result of Cardoso and Vodev, we show that the resolvent of the Laplacian on asymptotically hyperbolic manifolds is analytic in an exponential neighbourhood of the critical line. The case of non-trapping metrics with…
We prove that the Gromov boundary of every hyperbolic group is homeomorphic to some Markov compactum. Our reasoning is based on constructing a sequence of covers of $\partial G$, which is quasi-$G$-invariant wrt. the ball $N$-type (defined…
We provide detailed local descriptions of stable polynomials in terms of their homogeneous decompositions, Puiseux expansions, and transfer function realizations. We use this theory to first prove that bounded rational functions on the…
We obtain effective estimates for the growth rate of the $L^2$-energy of harmonic functions on geodesic balls in complete simply connected non-positively curved Riemannian manifolds with pinched sectional curvature. Our study relies upon a…
For closed and connected subgroups G of SO(n), we study the energy functional on the space of G-structures of a (compact) Riemannian manifold M, where G-structures are considered as sections of the quotient bundle O(M)/G. Then, we deduce…
The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the…
The stress tensor is a basic local operator in any field theory; in the context of AdS/CFT, it is the operator which is dual to the bulk geometry itself. Here we exploit this feature by using the bulk geometry to place constraints on the…
We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds…
This paper addresses the three concepts of \textit{ consistency, stability and convergence } in the context of compact finite volume schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of…