Related papers: The Abresch-Rosenberg Shape Operator and applicati…

We extend the so-called Kotani Theory for a particular class of ergodic matrix-like Jacobi operators defined in $l^{2}(\mathbb{Z}; \mathbb{C}^{l})$ by the law $[H_{\omega} \textbf{u}]_{n} := D^{*}(T^{n - 1}\omega) \textbf{u}_{n - 1} +…

Given a separable unital C*-algebra A, let E denote the Banach-space completion of the A-valued Schwartz space on Rn with norm induced by the A-valued inner product $<f,g>=\int f(x)^*g(x) dx$. The assignment of the pseudodifferential…

A model operator $H$ corresponding to a three-particle discrete Schr\"odinger operator on a lattice $\Z^3$ is studied. The essential spectrum is described via the spectrum of two Friedrichs models with parameters $h_\alpha(p),$…

It is proved that the holomorphic quadratic differential associated to CMC surfaces in Riemannian products $\mathbb{S}^2\times\Rr$ and $\mathbb{H}^2\times \Rr$ discovered by U. Abresch and H. Rosenberg could be obtained as a linear…

In this paper we study the behavior of the scalar curvature $S$ of a complete hypersurface immersed with constant mean curvature into a Riemannian space form of constant curvature, deriving a sharp estimate for the infimum of $S$. Our…

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of…

We describe the strong dual space $({\mathcal O} (D))^*$ for the space ${\mathcal O} (D)$ of holomorphic functions of several complex variables over a bounded Lipschitz domain $D$ with connected boundary $\partial D$ (as usual, ${\mathcal…

We study the inverse spectral problem for periodic Schr\"odinger opera\-tors of kind $- \frac{1}{2} \hbar^2 \Delta_x + V(x)$ on the flat torus $\Bbb T^n := (\Bbb R / 2 \pi \Bbb Z)^n$ with potentials $V \in C^{\infty} (\Bbb T^n)$. We show…

Following earlier work of Loftin-McIntosh, we study minimal Lagrangian immersions of the universal cover of a closed surface (of genus at least 2) into CH2, with prescribed data of a conformal structure plus a holomorphic cubic…

A real reductive pair $(G,H)$ is called strongly spherical if the homogeneous space $(G\times H)/{\rm diag}(H)$ is real spherical. This geometric condition is equivalent to the representation theoretic property that ${\rm…

In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth…

We investigate a reverse Faber-Krahn type inequality for the Robin Laplacian in a bounded smooth domain $\Omega \subset \mathbb{R}^N$ whose boundary has two connected components. We prove that a concentric spherical shell maximizes the…

Laurent Hauswirth and Harold Rosenberg developed the theory of minimal surfaces with finite total curvature in $\H^2\times\R$. They showed that the total curvature of one such a surface must be a non-negative integer multiple of $-2\pi$.…

A shape invariant nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined with the purpose of exhibiting its hidden algebraic structure.…

Suppose B=F[x,y,z]/h is the homogeneous coordinate ring of a characteristic p degree 3 irreducible plane curve C with a node. Let J be a homogeneous (x,y,z)-primary ideal and n -> e_n be the Hilbert-Kunz function of B with respect to J. Let…

We consider a periodic magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a noncompact Riemannian manifold $M$ such that $H^1(M, {\mathbb R})=0$ endowed with a properly discontinuous cocompact…

First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of…

We examine two types of half-BPS surface defects $-$ regular monodromy surface defect and canonical surface defect $-$ in four-dimensional gauge theory with $\mathcal{N}=2$ supersymmetry and…

For a Finsler metric $F$, we introduce the notion of $F$-covariant coefficients $H_i$ of the geodesic spray of $F$ (Def. 3.1). We study some geometric consequences concerning the objects $H_i$. If the $F$-covariant coefficients $H_i$ are…

For $0<k<1$, a finite-type $k$-surface in $3$-dimensional hyperbolic space is a complete, immersed surface of finite area and of constant extrinsic curvature equal to $k$. In [32], we showed that such surfaces have finite genus and finitely…