Families of Conformally Covariant Differential Operators, Q-Curvature and Holography

@inproceedings{Juhl2009FamiliesOC,
  title={Families of Conformally Covariant Differential Operators, Q-Curvature and Holography},
  author={A. Juhl},
  year={2009}
}
Spaces, Actions, Representations and Curvature.- Conformally Covariant Powers of the Laplacian, Q-curvature and Scattering Theory.- Paneitz Operator and Paneitz Curvature.- Intertwining Families.- Conformally Covariant Families. 
Singular invariant trilinear forms and covariant (bi-)differential operators under the conformal group
Abstract The residues of the meromorphic family of conformally invariant trilinear forms on the sphere (constructed in Clerc and Orsted, in press, [2] ) are computed. Their expression involvesExpand
Families of equivariant differential operators and anti de Sitter spaces
We prove existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces.Expand
Admissible $Q-$curvatures under isometries for the conformal GJMS operators
We give sufficient conditions on a function invariant under the action of an isometry group to be Branson's Q-curvature of a metric in a given conformal class, using the conformal GJMS operators.
Classification of differential symmetry breaking operators for differential forms
We give a complete classification of conformally covariant differential operators between the spaces of differential i-forms on the sphere Sn and j-forms on the totally geodesic hypersphere Sn−1 byExpand
Vector-Valued Covariant Differential Operators for the Möbius Transformation
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitraryExpand
Singular Solutions of Fractional Order Conformal Laplacians
We investigate the singular sets of solutions of a natural family of conformally covariant pseudodifferential elliptic operators of fractional order, with the goal of developing generalizations ofExpand
Extrinsic curvature and conformal Gauss-Bonnet for four-manifolds with corner
This paper defines two new extrinsic curvature quantities on the corner of a four-dimensional Riemannian manifold with corner. One of these is a pointwise conformal invariant, and the conformalExpand
Families of Equivariant Differential Operators and Anti-de Sitter Spaces
We prove the existence and uniqueness of a sequence of differential intertwining operators for principal series representations, which are realized on boundaries of anti-de Sitter spaces.Expand
Constant Q-curvature metrics near the hyperbolic metric
Abstract Let ( M , g ) be a Poincare–Einstein manifold with a smooth defining function. In this note, we prove that there are infinitely many asymptotically hyperbolic metrics with constantExpand
Q curvature and gravity
In this paper, we consider a family of $n$-dimensional, higher-curvature theories of gravity whose action is given by a series of dimensionally extended conformal invariants. The latter correspond toExpand
...
1
2
3
4
5
...