CMC Spheres in the Heisenberg Group

We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture. We also focus our attention on the sub-Riemannian limit

Ecological change, sliding baselines and the importance of historical data: Lessons from combing observational and quantitative data on a temperate reef over 70 years

Understanding the effects of environmental change on ecosystems requires the identification of baselines that may act as reference conditions. However, the continuous change of these references challenges our ability to define the true natural status of ecosystems. The so-called sliding baseline syndrome can be overcome through the analysis of quantitative time series, which are, however, extremely rare. Here we show how combining historical quantitative data with descriptive 'naturalistic' information arranged in a chronological chain allows highlighting long-term trends and can be used to inform present conservation schemes.We analysed the long-term change of a coralligenous reef, a marine habitat endemic to the Mediterranean Sea. The coralligenous assemblages of Mesco Reef (Ligurian Sea, NW Mediterranean) have been studied, although discontinuously, since 1937 thus making available both detailed descriptive information and scanty quantitative data: while the former was useful to understand the natural history of the ecosystem, the analysis of the latter was of paramount importance to provide a formal measure of change over time. Epibenthic assemblages remained comparatively stable until the 1990s, when species replacement, invasion by alien algae, and biotic homogenisation occurred within few years, leading to a new and completely different ecosystem state. The shift experienced by the coralligenous assemblages of Mesco Reef was probably induced by a combination of seawater warming and local human pressures, the latter mainly resulting in increased water turbidity; in turn, cumulative stress may have favoured the establishment of alien species. This study showed that the combined analysis of quantitative and descriptive historical data represent a precious knowledge to understand ecosystem trends over time and provide help to identify baselines for ecological management

PILOT APPLICATION OF 3D UNDERWATER IMAGING TECHNIQUES FOR MAPPING <i>POSIDONIA OCEANICA</i> (L.) DELILE MEADOWS

Seagrass communities are considered one of the most productive and complex marine ecosystems. Seagrasses belong to a small group of 66 species that can form extensive meadows in all coastal areas of our planet. Posidonia oceanica beds are the most characteristic ecosystem of the Mediterranean Sea, and should be constantly monitored, preserved and maintained, as specified by EU Habitats Directive for priority habitats. Underwater 3D imaging by means of still or video cameras can allow a detailed analysis of the temporal evolution of these meadows, but also of the seafloor morphology and integrity. Video-photographic devices and open source software for acquiring and managing 3D optical data rapidly became more and more effective and economically viable, making underwater 3D mapping an easier task to carry out. 3D reconstruction of the underwater scene can be obtained with photogrammetric techniques that require just one or more digital cameras, also in stereo configuration. In this work we present the preliminary results of a pilot 3D mapping project applied to the P. oceanica meadow in the Marine Protected Area of Capo Rizzuto (KR, Calabria Region &ndash; Italy)

On the isoperimetric problem in the Heisenberg group \u210dn

It has been recently conjectured that, in the context of the Heisenberg groupHn endowed with its Carnot\u2013Carath\ue9odory metric and Haar measure, the isoperimetricsets (i.e., minimizers of the H-perimeter among sets of constant Haar measure) couldcoincide with the solutions to a \u201crestricted\u201d isoperimetric problem within the class ofsets having finite perimeter, smooth boundary, and cylindrical symmetry. In this paper,we derive new properties of these restricted isoperimetric sets, which we call Heisenbergbubbles. In particular, we show that their boundary has constant mean H-curvature and, quitesurprisingly, that it is foliated by the family of minimal geodesics connecting two specialpoints. In view of a possible strategy for proving that Heisenberg bubbles are actuallyisoperimetric among the whole class of measurable subsets of Hn, we turn our attentionto the relationship between volume, perimeter, and -enlargements. In particular, we provea Brunn\u2013Minkowski inequality with topological exponent as well as the fact that the Hperimeterof a bounded, open set F 82 Hn of class C2 can be computed via a generalizedMinkowski content, defined by means of any bounded set whose horizontal projection is the2n-dimensional unit disc. Some consequences of these properties are discussed

Consequences of the marine climate and ecosystem shift of the 1980-90s on the Ligurian Sea biodiversity (NW Mediterranean Sea)

A rapid temperature increase in the 1980-90s has been accompanied by dramatic and unprecedented changes in the biota and communities of the Ligurian Sea. This review uses existing historical series (a few of which have been purposely updated) to assess extent and consequences of such changes. A number of warm-water species, previously absent or occasional in the comparatively cold Ligurian Sea, has recently established thanks to warmer winters. Occurrence among them of invasive alien species is causing concern because of their capacity of outcompeting autochthonous species. Summer heatwaves, on the other hand, caused mass mortalities in marine organisms, some of which found refuge at depth. New marine diseases appeared, as well as other dysfunctions such as the formation of mucilage aggregates that suffocated and entangled benthic organisms. Human pressures have combined with climate change to cause phase shifts (i.e., abrupt variations in species composition and community structure) in different habitats, such as the pelagic environment, seagrass meadows, rocky reefs, and marine caves. These phase shifts implied biotic homogenization, reduction of diversity, and dominance by invasive aliens, and may be detrimental to the resilience of Ligurian Sea ecosystems. Another phase of rapid warming has possibly started in the 2010s and there are clues pointing to a further series of biological changes, but data are too scarce to date for proper assessment. Only well addressed long-term studies will help understanding the future dynamics of Ligurian Sea ecosystems and their possibilities of recovery

First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds

We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator for non-singular C^2 surfaces and another one for C2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly changed and Remark 9.9 adde

Il coralligeno toscano: distribuzione, struttura dei popolamenti e monitoraggio mediante utilizzo di differenti indici di qualit\ue0 ecologica.

Coralligenous reefs are one of the main habitat of the Mediterranean Sea for distribution, biodiversity and role in the carbon cycle. Distribution and ecological quality of coralligenous reefs must be assessed under the Marine Strategy Framework Directive. The present work aimed at assess the distribution of coralligenous reefs in Tuscany waters, describing their structure and evaluating their ecological quality through different ecological quality indices. In Tuscany waters, coralligenous reefs are distributed on rocky cliffs between 25-30 m and 50-60 m of depth. The ecological quality resulted always sufficient with values of the indices higher on the islands than on the continental coasts

Climate change and Mediterranean seagrass meadows: A synopsis for environmental managers

This synopsis focuses on the effects of climate change on Mediterranean seagrasses, and associated communities, and on the contribution of the main species, Posidonia oceanica, to the mitigation of climate change effects through sequestering carbon dioxide. Whilst the regression of seagrass meadows is well documented, generally linked to anthropogenic pressures, global warming could be a cause of new significant regression, notably linked to the introduction of exotic species, the rise of Sea-Surface Temperature (SST), and relative sea level. Seagrass communities could also be affected by climate change through the replacement of high structural complexity seagrass species by species of lower complexity and even by opportunistic introduced species. Although it is currently very difficult to predict the consequences of these alterations and their cascade effects, two main potential conflicting trends in the functioning of seagrass ecosystems are acceleration of the herbivore pathway or the detritivore pathway. The mean net primary production of the dominant species, Posidonia oceanica, is relatively high and can be estimated to range between 92.5 to 144.7 g C m-2 a-1. Around 27% of the total carbon fixed by this species enters the sedimentary pathway leading to formation, over millennia, of highly organic deposits, rich in refractory carbon. At the Mediterranean scale, the sequestration rate might reach 1.09 Tg C a-1. The amount of this stored carbon is estimated to range from 71 to 273 kg C m-2, which when considered at the Mediterranean scale would represent 11 to 42% of the CO2 emissions produced by Mediterranean countries since the beginning of the Industrial Revolution. The greatest value of the P. oceanica ecosystem, in the context of mitigation of global climate change, is linked to this vast long-term carbon stock accumulated over millennia, and therefore, efforts should be focused on preserving the meadows to keep this reservoir intact