Displaying similar documents to “Conformally bending three-manifolds with boundary”

Quaternionic contact structures in dimension 7

David Duchemin (2006)

Annales de l’institut Fourier

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The conformal infinity of a quaternionic-Kähler metric on a 4 n -manifold with boundary is a codimension 3 distribution on the boundary called quaternionic contact. In dimensions 4 n - 1 greater than 7 , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7 , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact...

Extremal domains for the first eigenvalue of the Laplace-Beltrami operator

Frank Pacard, Pieralberto Sicbaldi (2009)

Annales de l’institut Fourier

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We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Riemannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.

Monopole metrics and the orbifold Yamabe problem

Jeff A. Viaclovsky (2010)

Annales de l’institut Fourier

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We consider the self-dual conformal classes on n # ℂℙ 2 discovered by LeBrun. These depend upon a choice of n points in hyperbolic 3 -space, called monopole points. We investigate the limiting behavior of various constant scalar curvature metrics in these conformal classes as the points approach each other, or as the points tend to the boundary of hyperbolic space. There is a close connection to the orbifold Yamabe problem, which we show is not always solvable (in contrast to the case of compact...