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Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
Abstract We give a detailed description of the Schwartz kernel of the resolvent of the Laplacian on a certain class of complete Riemannian manifolds with negative sectional curvature near infinity.Expand
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Refined asymptotics for constant scalar curvature metrics with isolated singularities
Abstract. We consider the asymptotic behaviour of positive solutions u of the conformal scalar curvature equation, , in the neighbourhood of isolated singularities in the standard Euclidean ball.Expand
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Kahler-Einstein metrics with edge singularities
This article considers the existence and regularity of Kahler-Einstein metrics on a compact Kahler manifold $M$ with edge singularities with cone angle $2\pi\beta$ along a smooth divisor $D$. WeExpand
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The Hodge cohomology of a conformally compact metric
On etudie le Laplacien de Hogde agissant sur des k-formes differentielles pour une classe de varietes de Riemann completes a courbure sectionnelle negative proche de l'infini. Ces varietes ont desExpand
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PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH FIBRED BOUNDARIES
Let X be a compact manifold with boundary. Suppose that the boundary is fibred, : @X! Y, and let x2C 1 (X) be a boundary defining function. This data fixes the space of 'fibred cusp' vector fields,Expand
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A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis
The aim of this paper is to prove the existence of weak solutions to the equation ∆u+u = 0 which are positive in a domain Ω ⊂ R , vanish at the boundary, and have prescribed isolated singularities.Expand
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Hodge cohomology of gravitational instantons
This article was published in the Duke Mathematical Journal [© Duke University Press] and is also available at: http://projecteuclid.org/euclid.dmj/1082665286
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Constant scalar curvature metrics with isolated singularities
We extend the results and methods of [6] to prove the existence of constant positive scalar curvature metrics g which are complete and conformal to the standard metric on S \ Λ, where Λ is a disjointExpand
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Analytic surgery and the eta invariant
AbstractLet (M, h) be an odd-dimensional compact spin manifold in whichH is an embedded hypersurface with quadratic defining functionx2∈C∞ (M). Let be the Dirac operator associated to the metric jhenExpand
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