# 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.

#### 113 Citations

Singular invariant trilinear forms and covariant (bi-)differential operators under the conformal group

- Mathematics
- 2012

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 involves… Expand

Families of equivariant differential operators and anti de Sitter spaces

- Mathematics
- 2008

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

- Mathematics
- 2010

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

- Mathematics
- 2016

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 by… Expand

Vector-Valued Covariant Differential Operators for the Möbius Transformation

- Mathematics
- 2014

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 arbitrary… Expand

Singular Solutions of Fractional Order Conformal Laplacians

- Mathematics
- 2009

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 of… Expand

Extrinsic curvature and conformal Gauss-Bonnet for four-manifolds with corner

- Mathematics
- 2020

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 conformal… Expand

Families of Equivariant Differential Operators and Anti-de Sitter Spaces

- 2009

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

- Mathematics
- 2012

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 constant… Expand

Q curvature and gravity

- Physics, Mathematics
- 2018

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 to… Expand