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Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus
Abstract: We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differentialExpand
The ambient obstruction tensor and the conformal deformation complex
We construct here a conformally invariant differential operator on algebraic Weyl tensors that gives special curved analogues of certain operators related to the deformation complex and that, uponExpand
Conformal boundary operators, T-curvatures, and conformal fractional Laplacians of odd order
We construct continuously parametrised families of conformally invariant boundary operators on densities. These may also be viewed as conformally covariant boundary operators on functions andExpand
Future Directions of Research in Geometry: A Summary of the Panel Discussion at the 2007 Midwest Geometry Conference
The 2007 Midwest Geometry Conference included a panel discussion devoted to open problems and the general direction of future research in fields related to the main themes of the conference. ThisExpand
Conformally covariant pseudo-differential operators
Abstract We construct an intrinsically defined conformally covariant pseudo-differential operator of arbitrary real-number order acting on scalar functions. In even dimensions the operator is onlyExpand
A conformally invariant Yang-Mills type energy and equation on 6-manifolds
We define a conformally invariant action S on gauge connections on a closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the gauge connection. The Euler-LagrangeExpand