Bifurcation of periodic solutions to the singular Yamabe problem on spheres

We obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere, that blow up along a great circle. These are (complete) constant scalar curvature metrics on the complement of $S^1$ inside $S^m$, $m\geq 5$, that are conformal to the round (incomplete) metric and "periodic" in the sense of being invariant under a discrete group of conformal transformations. These solutions come from bifurcating branches of constant scalar curvature metrics on compact quotients of $S^m \setminus S^1\cong S^{m-2}\times H^2$.Comment: LaTeX2e, 12 pages, final version. To appear in J. Differential Geo

Asymptotic behavior of complete Ricci-flat metrics on open manifolds

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 59-60).In this thesis, we describe the asymptotic behavior of complete Ricci-flat Kihler metrics on open manifolds that can be compactified by adding a smooth, ample divisor. This result provides an answer to a question addressed to by Tian and Yau in [TY1], therefore refining the main result in that paper.by Bianca Santoro.Ph.D

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201

Contraception in chronic kidney disease: a best practice position statement by the Kidney and Pregnancy Group of the Italian Society of Nephrology

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