Strong unique continuation for general elliptic equations in 2D

We prove that solutions to elliptic equations in two variables in divergence form, possibly non-selfadjoint and with lower order terms, satisfy the strong unique continuation property.Comment: 10 page

Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure

Holomorphic submersions onto K\"ahler or balanced manifolds

We study many properties concerning weak K\"ahlerianity on compact complex manifolds which admits a holomorphic submersion onto a K\"ahler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the K\"ahler case), Michelson (the balanced case), Popovici (the sG case) and others.Comment: 14 pages; second revised version; in press, Tohoku Math. J. vol 68, n.4 (2016

Tropicalization of group representations

In this paper we give an interpretation to the boundary points of the compactification of the parameter space of convex projective structures on an n-manifold M. These spaces are closed semi-algebraic subsets of the variety of characters of representations of the fundamental group of M in SL_{n+1}(R). The boundary was constructed as the tropicalization of this semi-algebraic set. Here we show that the geometric interpretation for the points of the boundary can be constructed searching for a tropical analogue to an action of the group on a projective space. To do this we need to construct a tropical projective space with many invertible projective maps. We achieve this using a generalization of the Bruhat-Tits buildings for SL_{n+1} to non-archimedean fields with real surjective valuation. In the case n = 1 these objects are the real trees used by Morgan and Shalen to describe the boundary points for the Teichmuller spaces. In the general case they are contractible metric spaces with a structure of tropical projective spaces.Comment: 27 pages, 1 figure; Changes in version 2: minor changes, some references added. Changes in version 3: the paper has been updated according to the companion paper arXiv:0801.0165 v1, some typos correcte

The Role of the Euro-Mediterranean Relations Facing the Economic Crisis

The global financial crisis is affecting the Mediterranean Countries in seveal ways: a slowdown in global economic growth, a decline in foreign direct investment inflows, a decline of worker remittances. However, their economies continued to show more sustainable growth in the face of rapidly changing external macroeconomic conditions. In this context, the Union for the Mediterranean set up four priorities for the Southern partners: SMEs, high unemployment, increasing environmental strains and inefficient transport infrastructures. This is a high profile initiative, but based on voluntary contributions. For this reason it is hardly difficult to identify the amount of financial resources that will be mobilised and their economic and social impact.Union for the Mediterranean, Financial resources, FTA