Minimal surfaces - variational theory and applications

Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject is characterized by a profound beauty, but perhaps even more remarkably, minimal surfaces (or minimal submanifolds) have encountered striking applications in other fields, like three-dimensional topology, mathematical physics, conformal geometry, among others. Even though it has been the subject of intense activity, many basic open problems still remain. In this lecture we will survey recent advances in this area and discuss some future directions. We will give special emphasis to the variational aspects of the theory as well as to the applications to other fields.Comment: Proceedings of the ICM, Seoul 201

Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature

We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly positive scalar curvature on an orientable 3-manifold is path-connected. This generalizes the main result of the fourth author [Mar12] in the compact case. The proof uses Ricci flow with surgery as well as arguments involving performing infinite connected sums with control on the geometry

God and Creation: Trinity and Creation out of Nothing

The question of God’s relationship with creation touches upon important contemporary issues with regard to science, interfaith dialogue, and contemporary philosophy. Using the fundamental and specifically Christian theological stance that begins from creatio ex nihilo, the author shows how Chiara Lubich, on the basis of her charism of unity, develops an original understanding of the event of creation in which God creates by giving being to nonbeing, constantly creating historically and preserving in being what is created, and, at the same time, making what is created evolve. The basis for this understanding is to read creation out of nothing in light of a radical understanding of divine love that, as a result of its own dynamic, is both One and Three. This vision of reality implicitly contains a Trinitarian metaphysics that reinterprets the vestigia trinitatis in creation and gives a fresh understanding of creation’s vocation to share in the divine life

Creation in Christ and the New Creation in the Mysticism of Chiara Lubich

In a previous article, after illustrating the theological contexts of the classical tradition and of modern times that form the background of the vision of creation in Chiara Lubich’s mysticism, the author looked in particular at the meaning of “creation out of nothing” from the point of view of a Trinitarian ontology of love. Now he focuses with greater clarity upon creation in Christ, taking a closer look at the “new creation” in Christ crucified and risen and at our participation in it

An Investigation of the Diagnostic Potential of Autofluorescence Lifetime Spectroscopy and Imaging for Label-Free Contrast of Disease

The work presented in this thesis aimed to study the application of fluorescence lifetime spectroscopy (FLS) and fluorescence lifetime imaging microscopy (FLIM) to investigate their potential for diagnostic contrast of diseased tissue with a particular emphasis on autofluorescence (AF) measurements of gastrointestinal (GI) disease. Initially, an ex vivo study utilising confocal FLIM was undertaken with 420 nm excitation to characterise the fluorescence lifetime (FL) images obtained from 71 GI samples from 35 patients. A significant decrease in FL was observed between normal colon and polyps (p = 0.024), and normal colon and inflammatory bowel disease (IBD) (p = 0.015). Confocal FLIM was also performed on 23 bladder samples. A longer, although not significant, FL for cancer was observed, in paired specimens (n = 5) instilled with a photosensitizer. The first in vivo study was a clinical investigation of skin cancer using a fibre-optic FL spectrofluorometer and involved the interrogation of 27 lesions from 25 patients. A significant decrease in the FL of basal cell carcinomas compared to healthy tissue was observed (p = 0.002) with 445 nm excitation. A novel clinically viable FLS fibre-optic probe was then applied ex vivo to measure 60 samples collected from 23 patients. In a paired analysis of neoplastic polyps and normal colon obtained from the same region of the colon in the same patient (n = 12), a significant decrease in FL was observed (p = 0.021) with 435 nm excitation. In contrast, with 375 nm excitation, the mean FL of IBD specimens (n = 4) was found to be longer than that of normal tissue, although not statistically significant. Finally, the FLS system was applied in vivo in 17 patients, with initial data indicating that 435 nm excitation results in AF lifetimes that are broadly consistent with ex vivo studies, although no diagnostically significant differences were observed in the signals obtained in vivo.Open Acces

Rising groundwater levels in the Neapolitan area and its impacts on civil engineering structures, agricultural soils and archaeological sites

The rise of groundwater levels (GWLr) is a worldwide phenomenon with several consequences for urban and rural environment, cultural heritage and human health. In this thesis the phenomenon and its effects are analysed in two sectors of the Metropolitan City of Naples (southern Italy). These areas are the central sector of the eastern plain of Naples and the Cumae archaeological site in the western coastal sector of Phlegraean Fields. The triggering mechanism of GWLr is attributed to anthropogenic and natural causes, as the groundwater rebound (GR) process and the relative sea level rise due to volcano-tectonic subsidence of coastal areas. In the eastern plain of Naples, the interruption of pumping for public and private purposes occurred in 1990, leading to a progressive increase of piezometric levels with values up to 16.54 m. Since the end of 2000s, episodes of groundwater flooding (GF) have been registered on underground structures and agricultural soils. The historical piezometric levels and a comprehensive conceptual model of the aquifer have been reconstructed, as well as a first inventory of GF episodes and the hydrogeological controlling factors of GF occurrence have been detected. The economic consequences of GF have been analysed for an experimental building of study area, in which a sharp increment of expenditures has been registered. These costs include technical and legal support, construction and maintenance of GF mitigation measures and electricity consumption. Others GWLr-induced phenomena have been recognised, as ground vertical deformation and variations of the groundwater contamination. A relationship between GWLr and ground uplift emerges from the coupled analysis of piezometric and interferometric data, referred to the 1989-2013 period. The ground deformation occurs in response to the recovery of pore-pressure in the aquifer system, reaching an uplift magnitude up to 40-50 mm. In the 1989-2017 period, the piezometric levels and the concentrations of some natural contaminants in groundwater (Fe, Mn, fluorides) show opposite trends, conversely the same rising trend has been observed with nitrates. These different responses to piezometric rise are related to the lack of mobilization of deep fluids due to the interruption of pumping and to the reduction of the surficial contaminants' time travel caused by a shorter thickness of the vadose zone. In the western sector of Phlegraean Fields, the naturally triggered GWLr has caused GF in the Cumae archaeological site for the last decade, threatening safeguard and conservation of the archaeological heritage. From an integrated hydrogeological, hydrochemical and isotopic survey, a considerable contamination of groundwater resulted, due to the presence of rising highly mineralized fluids, mobilized during pumping periods, and others anthropogenic sources of contamination. Lastly, a novel methodology for groundwater flooding susceptibility (GFS) assessment has been developed by using machine learning techniques and tested in the eastern plain of Naples. Points of GF occurrence have been connected to environmental predisposing factors through Spatial Distribution Models' algorithms to estimate the most prone areas' distribution. Ensemble Models have been carried out to reduce the uncertainty associated with each algorithm and increase its reliability. Mapping of GFS has been realized by dividing occurrence probability values into five classes of susceptibility. Results show an optimal correspondence between GF points' location and the highest classes (93% of GF points falls into high and very high classes). The results of this research provide new knowledge on the GWLr phenomenon that has impacted a large territory of the Metropolitan City of Naples. The methodological approach used can be exported in others hydrogeological contexts to characterize GWLr and its impacts. In addition, the implemented GFS methodology represents a new tool to assist local government authorities, planners and water decision-makers in addressing the problems deriving from GF, and a first step for the evaluation of GF risk as required by Italian and European legislation

Chiara Lubich and the Theology of Jesus: The Trinity as Place, Method, and Object of Thinking

This article begins by outlining the variety of forms theology takes to illustrate that the key to theological knowledge is knowing God through participation in Jesus’ knowledge of God. This participation is apparent in scripture and theological tradition, and the author argues that the modern theological method, for all of its advances, must regain awareness of this participating, through Christ, in God’s self-knowledge. At the same time Coda presents the different gifts of the Spirit throughout history, namely, the charisms, and among these gives particular attention to Chiara Lubich’s charism of unity. Coda explains how this charism, via the experience of humans united in God, provides a participatory knowledge of God in which knowing and loving coincide. Various significant consequences are drawn from this participation. Coda then turns to the basis for this knowledge, namely, the forsakenness of Christ upon the cross, to show how the crucified intellect goes beyond its natural limitations to share in the intellect, the mind (nous), of Christ. Coda concludes with implications of this way of knowing for theological practice and suggests possibilities for a fresh approach that respects contemporary needs

Crossing the Threshold: Mission as Encounter

Awareness of the centrality of mission has been growing in the Catholic Church since Vatican II. The author traces this growth from Ecclesiam suam (1964) to the writings of the current pope, highlighting the link between dialogue and mission. He draws attention to some features of Francis’s message using four words: “kairos,” the “why,” “how,” and “where” of mission, and situates the ongoing dialogue between Catholics and Shia Islam within this broad framework

Revealed Religion’s Vital Contribution to the Epoch-Making Newness of a Culture of Unity

The author writes: “In memory of Bishop Pietro Rossano, that unforgettable and wise teacher in the past and in the present, about dialogue among religions, this article offers the text of a lecture titled ‘Unity of God, Unity in God.’ The lecture was part of a course organized by Sophia University Institute in Loppiano and the Islamic Centre of England in London with twenty Catholic university students and an equal number of Muslims. It was held at Tonadico (Trent) in September 2017. Among other things, I was inspired by the following affirmation of Bishop Rossano; it is like the hidden thread running through the thought I develop here. what writes that we need to express “the interpersonal relationship peculiar to the Christian faith, a relationship inviting subjects into a new relationship with God and their brothers or sisters in a form transcending the orbit of all religions because it is anchored in the mystery of the uni-triune God which humanity shares in Jesus Christ. Far from destroying the preceding religious heritage, this new rapport purifies and expands this heritage to formerly unknown horizons” (Il problema teologico delle religioni, Ed. Paoline, 1975, 46)