A soft Oka principle for proper holomorphic embeddings of open Riemann surfaces into (C∗)2(\mathbb{C}^*)^2

Let $X$ be an open Riemann surface. We prove an Oka property on the approximation and interpolation of continuous maps $X \to (\mathbb{C}^*)^2$ by proper holomorphic embeddings, provided that we permit a smooth deformation of the complex structure on $X$ outside a certain set. This generalises and strengthens a recent result of Alarcon and Lopez. We also give a Forstneric-Wold theorem for proper holomorphic embeddings (with respect to the given complex structure) of certain open Riemann surfaces into $(\mathbb{C}^*)^2$

A strong Oka principle for embeddings of some planar domains into CxC*

Gromov, in his seminal 1989 paper on the Oka principle, introduced the notion of an elliptic manifold and proved that every continuous map from a Stein manifold to an elliptic manifold is homotopic to a holomorphic map. We show that a much stronger Oka principle holds in the special case of maps from certain open Riemann surfaces called circular domains into CxC*, namely that every continuous map is homotopic to a proper holomorphic embedding. An important ingredient is a generalisation to CxC* of recent results of Wold and Forstneric on the long-standing problem of properly embedding open Riemann surfaces into C^2, with an additional result on the homotopy class of the embeddings. We also give a complete solution to a question that arises naturally in Larusson's holomorphic homotopy theory, of the existence of acyclic embeddings of Riemann surfaces with abelian fundamental group into 2-dimensional elliptic Stein manifolds.Comment: 25 page

Proper holomorphic immersions in homotopy classes of maps from finitely connected planar domains into CxC*

Gromov, in his seminal 1989 paper on the Oka principle, proved that every continuous map from a Stein manifold into an elliptic manifold is homotopic to a holomorphic map. Previously we have shown that, given a continuous map X \to \C\times\C^* from a finitely connected planar domain $X$ without isolated boundary points, a stronger Oka property holds, namely that the map is homotopic to a proper holomorphic embedding. Here we show that every continuous map from a finitely connected planar domain, possibly with punctures, into \C\times\C^* is homotopic to a proper immersion that identifies at most countably many pairs of distinct points, and in most cases, only finitely many pairs. By examining situations in which the immersion is injective, we obtain a strong Oka property for embeddings of some classes of planar domains with isolated boundary points. It is not yet clear whether a strong Oka property for embeddings holds in general when the domain has isolated boundary points. We conclude with some observations on the existence of a null-homotopic proper holomorphic embedding \C^* \to \C\times\C^*

Proper holomorphic embeddings into Stein manifolds with the density property

We prove that a Stein manifold of dimension $d$ admits a proper holomorphic embedding into any Stein manifold of dimension at least $2d+1$ satisfying the holomorphic density property. This generalizes classical theorems of Remmert, Bishop and Narasimhan pertaining to embeddings into complex Euclidean spaces, as well as several other recent results.Comment: To appear in J. d'Analyse Mat

Families of Proper Holomorphic Embeddings and Carleman-Type Theorem with parameters

We solve the problem of simultaneously embedding properly holomorphically into C2 a whole family of n-connected domains Omega_r in P1 such that none of the components of P1 \ Omega_r reduces to a point, by constructing a continuous mapping such that is a proper holomorphic embedding for every r. To this aim, a parametric version of both the Andersén–Lempert procedure and Carleman’s Theorem is formulated and proved.publishedVersio

Families of Proper Holomorphic Embeddings and Carleman-type Theorems with parameters

We solve the problem of simultaneously embedding properly holomorphically into $\Bbb C^2$ a whole family of $n$-connected domains $\Omega_r\subset\Bbb P^1$ such that none of the components of $\Bbb P^1\setminus\Omega_r$ reduces to a point, by constructing a continuous mapping $\Xi\colon\bigcup_r\{r\}\times\Omega_r\to\Bbb C^2$ such that $\Xi(r,\cdot)\colon\Omega_r\hookrightarrow\Bbb C^2$ is a proper holomorphic embedding for every $r$. To this aim, a parametric version of both the Anders\'en-Lempert procedure and Carleman's Theorem is formulated and proved

eHealth Parent Education for Hearing Aid Management: A Pilot Randomized Controlled Trial

Objective: Parents frequently experience challenges implementing daily routines important for consistent hearing aid management. Education that supports parents in learning new information and gaining confidence is essential for intervention success. We conducted a pilot study to test an eHealth program to determine if we could implement the program with adherence and affect important behavioral outcomes compared to treatment as usual. Design: Randomized controlled trial Study sample: Parents of children birth to 42 months who use hearing aids. Eighty-two parents were randomly assigned to the intervention or treatment-as-usual group. Four parents assigned to the intervention group did not continue after baseline testing. Results: The intervention was delivered successfully with low drop out (10%), high session completion (97%), and high program adherence. The intervention conditions showed significantly greater gains over time for knowledge, confidence, perceptions, and monitoring related to hearing aid management. Significant differences between groups were not observed for hearing aid use time. Conclusion: We found that we could successfully implement this eHealth program and that it benefitted the participants in terms of knowledge and confidence with skills important for hearing aid management.Future research is needed to determine how to roll programs like this out on a larger scale

Transport and structural study of pressure-induced magnetic states in Nd0.55Sr0.45MnO3 and Nd0.5Sr0.5MnO3

Pressure effects on the electron transport and structure of Nd1-xSrxMnO3 (x = 0.45, 0.5) were investigated in the range from ambient to ~6 GPa. In Nd0.55Sr0.45MnO3, the low-temperature ferromagnetic metallic state is suppressed and a low temperature insulating state is induced by pressure. In Nd0.5Sr0.5MnO3, the CE-type antiferromagnetic charge-ordering state is suppressed by pressure. Under pressure, both samples have a similar electron transport behavior although their ambient ground states are much different. It is surmised that pressure induces an A-type antiferromagnetic state at low temperature in both compounds

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

The study of the manganese oxides, widely known as manganites, that exhibit the ``Colossal'' Magnetoresistance (CMR) effect is among the main areas of research within the area of Strongly Correlated Electrons. After considerable theoretical effort in recent years, mainly guided by computational and mean-field studies of realistic models, considerable progress has been achieved in understanding the curious properties of these compounds. These recent studies suggest that the ground states of manganite models tend to be intrinsically inhomogeneous due to the presence of strong tendencies toward phase separation, typically involving ferromagnetic metallic and antiferromagnetic charge and orbital ordered insulating domains. Calculations of the resistivity versus temperature using mixed states lead to a good agreement with experiments. The mixed-phase tendencies have two origins: (i) electronic phase separation between phases with different densities that lead to nanometer scale coexisting clusters, and (ii) disorder-induced phase separation with percolative characteristics between equal-density phases, driven by disorder near first-order metal-insulator transitions. The coexisting clusters in the latter can be as large as a micrometer in size. It is argued that a large variety of experiments reviewed in detail here contain results compatible with the theoretical predictions. It is concluded that manganites reveal such a wide variety of interesting physical phenomena that their detailed study is quite important for progress in the field of Correlated Electrons.Comment: 76 pages, 21 PNG files with figures. To appear in Physics Report