An interesting family of conformally invariant one-forms in even dimensions

Conformally invariant trilinear forms on the sphere

To each complex number λ is associated a representation πλ of the conformal group SO0(1, n) on C∞(Sn−1) (spherical principal series). For three values λ1, λ2, λ3, we construct a trilinear form on C∞(Sn−1)×C∞(Sn−1)×C∞(Sn−1), which is invariant by πλ1 ⊗πλ2 ⊗ πλ3 . The trilinear form, first defined for (λ1, λ2, λ3) in an open set of C is extended meromorphically, with simple poles located in an ex...

Boundary Regularity for Conformally Compact Einstein Metrics in Even Dimensions

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson found in [And03] and [And06]. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. This, together with boundary conditions that the com...

Is mass conformally invariant ?

By using the Garfinkle, Horowitz and Strominger black hole solutions as examples, we illustrate that, with respect to the reference action functional proposed by Hawking and Horowitz, the asymp-totic mass parameter is not invariant between two conformally related static spherically symmetric metrics.

Minimization of Conformally Invariant Energies

Conformally Invariant Non-local Operators

On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant nonlocal operators on the boundary Σ, generalizing the conformal Dirichlet-to-Robin operator, with principal par...