Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces

Hassan Boualem; Marc Herzlich

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We describe all compact spin Kähler manifolds of even complex dimension and positive scalar curvature with least possible first eigenvalue of the Dirac operator.

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Let $M$ a compact connected oriented 4-manifold. We study the space $Ξ$ of ${Spin}^{c}$ -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on $M$ . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all ${Spin}^{c}$ -structures $Ξ$ . We prove that, on a complex Kähler surface, for an hermitian metric $h$ sufficiently close to the original Kähler metric, the...

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The positive mass theorem for ALE manifolds

Mattias Dahl (1997)

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