Construction of harmonic diffeomorphisms and minimal graphs

We study complete minimal graphs in HxR, which take asymptotic boundary values plus and minus infinity on alternating sides of an ideal inscribed polygon Γ in H. We give necessary and sufficient conditions on the "lenghts" of the sides of the polygon (and all inscribed polygons in Γ) that ensure the existence of such a graph. We then apply this to construct entire minimal graphs in HxR that are conformally the complex plane C. The vertical projection of such a graph yields a harmonic diffeomorphism from C onto H, disproving a conjecture of Rick Schoen

The topology, geometry and conformal structure of properly embedded minimal surfaces

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies, for instance, that the surface can have at most two limit ends (at the top and bottom of the ordering), which is a strong topological restriction. There are also restrictions on the asymptotic geometry and conformal structure of such a surface: for example, we prove that if the surface has exactly two limit ends (as do the classical Riemann Staircase examples), then it is recurrent (that is, almost all Brownian paths are dense in the surface, and in particular any positive harmonic function on the surface is constant). These results have played an important role in the proof of several recent advances in the theory, including the uniqueness of the helicoid, the invariance of flux for a coordinate function on a properly immersed minimal surface, and the topological classification of properly embedded minimal surfaces

Minimal surfaces in finite volume hyperbolic 3-manifolds N and in MxS(1), M a finite area hyperbolic surface

We consider properly immersed finite topology minimal surfaces S in complete finite volume hyperbolic 3-manifolds N, and in M x S(1), where M is a complete hyperbolic surface of finite area. We prove S has finite total curvature equal to 2\pi times the Euler characteristic of S, and we describe the geometry of the ends of S

L’acteur d’une langue

Ce qui n’est pas de l’art n’est rien, quoi qu’ils en disent. Une singerie formelle (oui, formelle, voilà bien l’unique et total formalisme) où les hommes repus (la majorité) croient se reconnaître parce qu’elle semble leur parler. Il est si reposant de faire semblant dans ce monde de faux-semblant. Ne soyez pas de ce semblant-là, si c’est possible. Évitez-le, si c’est possible encore. Soyez, si c’est possible, et chacun à votre rythme, à votre f..

Plasmon dispersion diagram and localization effects in a three-cavity commensurate grating

International audienceCommensurate gratings of deep-metallic grooves have highly localized cavity resonances which do not exist for purely periodic gratings. In this paper we present the experimental dispersion diagram of the reso- nances of a commensurate grating with three sub-wavelength cavities per period. We observe selective light localization within the cavities, transition from a localized to a delocalized mode and modifications of the coupling of modes with the external plane-wave that may lead to the generation of black modes. This unexpected complexity is analyzed via a theoretical study in full agreement with the experiments. These results open a way to the control of wavelength-dependent hot spot predicted in more complex commensurate grating

Evaluation of Belgian clays for manufacturing compressed earth blocks

This study aims to characterize Belgian clays in order to evaluate their use for manufacture of compressed earth blocks (CEBs)

Clinical and MRI outcomes 10 years after repair of massive posterosuperior rotator cuff tears

BACKGROUND: Massive rotator cuff tears are challenging to treat, with few or no studies on long-term outcomes of repair. The purpose of this study was to report 10-year outcomes following repair of massive posterosuperior rotator cuff tears, with and without extension into the subscapularis, and to determine prognostic factors that could influence clinical scores and retear rates. METHODS: The records of 234 patients who underwent repair of a massive posterosuperior rotator cuff tear at a total of 15 centers were retrieved. Patients were asked to return for evaluation at 10 years; 78 patients could not be contacted, 7 had died, and 19 had undergone a reoperation. A total of 130 patients (68% men) with a mean age (and standard deviation) of 56.1 ± 7.7 years (range, 26 to 79 years) were evaluated clinically, and 102 of them were also evaluated using magnetic resonance imaging (MRI). The tear was confined to the supraspinatus and infraspinatus tendons in 94 shoulders and also involved the superior portion of the subscapularis in 36 shoulders. Univariable and multivariable regressions were performed to determine whether 10-year total Constant-Murley scores and repair integrity were associated with patient characteristics, tear patterns, or repair techniques. RESULTS: In the study cohort, complications were noted in 14 shoulders (11%) (stiffness in 10 and infection in 4). For the 130 shoulders evaluated clinically, the mean total Constant-Murley score improved from 53.1 ± 15.9 (range, 14 to 83) preoperatively to 78.5 ± 11.3 (range, 36 to 98) at 10 years. Of the 102 shoulders evaluated using MRI, 32 had a retear (Sugaya type IV or V). Of the 19 shoulders that underwent a reoperation (excluded from the study cohort), 9 had a retear. The overall prevalence of retears was 34%. Multivariable regression analysis revealed a significant association between the 10-year Constant-Murley score and preoperative retraction of the infraspinatus tendon, but no association between retears and any of the variables. Involvement of the subscapularis had no significant effect on preoperative or postoperative Constant-Murley scores or retear rates. CONCLUSIONS: Patients who had repair of a massive posterosuperior rotator cuff tear maintained considerable improvements in clinical and radiographic outcomes at 10 years. Partial concomitant tears of the subscapularis did not affect the total postoperative Constant-Murley scores or retear rates

The ocean sampling day consortium.

Ocean Sampling Day was initiated by the EU-funded Micro B3 (Marine Microbial Biodiversity, Bioinformatics, Biotechnology) project to obtain a snapshot of the marine microbial biodiversity and function of the world's oceans. It is a simultaneous global mega-sequencing campaign aiming to generate the largest standardized microbial data set in a single day. This will be achievable only through the coordinated efforts of an Ocean Sampling Day Consortium, supportive partnerships and networks between sites. This commentary outlines the establishment, function and aims of the Consortium and describes our vision for a sustainable study of marine microbial communities and their embedded functional traits