We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the affine three-space, and constant mean curvature one surfaces and flat surfaces in hyperbolic three-space. To achieve this purpose, we prove an optimal curvature bound for a specified conformal metric on an open Riemann surface and give some applications. We also provide unicity theorems for the Gauss maps of these classes of surfaces.

We show that an enslaved phase-separation front moving with diffusive speeds can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. To our knowledge this is the first fully analytical derivation of the Liesegang laws. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

Nous étudions expérimentalement la dynamique de mousses élastiques (mousse ouverteflexible en polyuréthane) plongées dans un fluide visqueux. La mousse est initialementcomprimée dans une direction puis brutalement relâchée. Le champ de vitesse de la mousseet la pression du fluide interstitiel (pression de pore) sont mesurés au cours de ladécompaction du système. Pour des petites compactions initiales, on observe que la mousserelaxe exponentiellement vers son état d’équilibre, avec une dynamique diffusive en accordquantitatif avec les théories classiques de consolidation des sols. En revanche, pour desgrandes compactions initiales, la dynamique de relaxation est inhomogène et se déroule àtravers un front de décompaction. Un modèle diphasique simple permet de prédiresemi-quantitativement les observations et relie l’existence du front au caractèrefortement non-linéaire de la réponse mécanique de la mousse.

During January-March, 1991, the distribution and floristic composition of the phytoplankton around Elephant Island, Clarence Island and the northern end of King George Island were determined in relation to physical oceanographic conditions and to proximity of the shelf-break and continental slope. The study area included 180 stations, and c. 5400 km of transects providing continuous measurements of salinity, temperature, beam attenuation, and chlorophyll a (chl a) concentrations in surface waters. The richest phytoplankton areas (2-4 μg chl a 1-1) were generally found associated with a strong salinity front, extending north of King George Island to north of Elephant and Clarence Islands. Data on the phytoplankton community suggest that shelf waters were charaterized by low biomass and a nanoplankton population, while in and just north of the front the biomass increased and there was a shift to a diatom-dominated microplankton population. This is thought to be related to increased stability of the water column just north of the front. The salinity front ran more or less parallel to the continental shelf-break, but its exact position varied during the period of study. It was generally associated with transition water (Type II) or with Weddell-Scotia Confluence water (Type III).