The Codazzi Equation for Surfaces

In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms {\bb R}^3, {\bb S}^3 and {\bb H}^3. We give essentially sharp generalizations of some classical theorems of surface theory that mainly depend on the Codazzi equation, and we apply them to the study of Weingarten surfaces in space forms. In particular, we study existence of holomorphic quadratic differentials, uniqueness of immersed spheres in geometric problems, height estimates, and the geometry and uniqueness of complete or properly embedded Weingarten surfaces

Isolated singularities of the prescribed mean curvature equation in Minkowski 33-space

We give a classification of non-removable isolated singularities for real analytic solutions of the prescribed mean curvature equation in Minkowski $3$-space

On the Generalized Weyl Problem for Flat Metrics in the Hyperbolic 3-space

Abstract The paper deals with the study of complete embedded flat surfaces in H 3 with a finite number of isolated singularities. We give a detailed information about its topology, conformal type and metric properties. We show how to solve the generalized Weyl's problem of realizing isometrically any complete flat metric with Euclidean singularities in H 3 which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities

Experimental set-up for exciting and detecting magneto-optical effects and surface plasmon resonance simultaneously

We present here an experimental set-up system to excite and measure simultaneously surface plasmon resonance (SPR) and magneto-optic signal in hybrid magneto-plasmonic systems using two independent light sources. The system can be used to excite and measure both types of SPR, localized surface plasmons in nanostructures and surface plasmon polaritons in thin films. It also allows measuring SPR in presence of magnetic fields and recording magnetooptical hysteresis loops while exciting SPR

Isometric immersions of L 2 into L 4

Abstract We give a global Weierstrass representation for isometric immersions with flat normal bundle from domains of the Lorentz plane L 2 into L 4 . This representation relies on the choice of two holomorphic data on a Riemann surface, and the integration of a hyperbolic linear differential system. As applications, we give classification results and construct complete examples in explicit coordinates by exact integration of the differential system for some particular choices of the holomorphic data