1,721,073 research outputs found
Rigidity and compactness with constant mean curvature in warped product manifolds
No full textWe prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in general relativity, like the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds). As a corollary, we characterize limits of rectifiable boundaries whose mean curvatures converge, as distributions, to a constant. The latter result is new, and requires the full strength of distributional CMC-rigidity, even when one considers smooth boundaries whose mean curvature oscillations vanish in arbitrarily strong C k C^{k} -norms. Our method also establishes that rectifiable boundaries of sets of finite perimeter in the hyperbolic space with constant distributional mean curvature are finite unions of possibly mutually tangent geodesic spheres
A mass transportation approach to quantitative isoperimetric inequalities
No full textA sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov’s proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary
Talesun Solar Bond: where securitization meets project financing
No full textIn July 2016, TS Energy Italy SpA, the subsidiary of a Chinese multinational group active in the renewable energy sector, structured a transaction called "Project Caesar" involving the issuance of a €40 million project bond. The Bond served to refinance part of the Issuer's Italian assets, consisting in a portfolio of 39 photovoltaic plants owned by several SPVs controlled by TS Energy Italy SpA. The case is useful to analyze the characteristics of a project finance asset backed security from the perspective of a fixed income investor. With the analysis of the issuer re-organization preliminary to the bond issuance, along with the data on the project’s portfolio and the fixed rate senior secured notes, the reader can perform the tasks of a bond investor who needs to assess the strengths and weaknesses of the deal. The case is also informative with respect to the progressive convergence of traditional project finance schemes with the securitization market
Improved convergence theorems for bubble clusters. II. The three-dimensional case
Full text linkGiven a sequence of almost-minimizing clusters in that converges in to a limit cluster , we prove the existence of -diffeomorphisms between and that converge in to the identity. Each of these boundaries is divided into -surfaces of regular points, -curves of points of type (where the boundary blows up to three half-spaces meeting along a line at 120 degree), and isolated points of type (where the boundary blows up to the two-dimensional cone over a one-dimensional regular tetrahedron). The diffeomorphisms are compatible with this decomposition, in the sense that they bring regular points into regular points and singular points of a kind into singular points of the same kind. They are almost-normal, meaning that at fixed distance from the set of singular points, each is a normal deformation of , and at fixed distance from the points of type , is a normal deformation of the set of points of type . Finally, the tangential displacements are quantitatively controlled by the normal displacements. This improved convergence theorem is then used in the study of isoperimetric clusters in
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