Related papers: GJMS operators and Q-curvature for conformal Codaz…

We derive extrinsic GJMS operators and $Q$-curvatures associated to a submanifold of a conformal manifold. The operators are conformally covariant scalar differential operators on the submanifold with leading part a power of the Laplacian…

We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincar\'e-Einstein metrics and renormalized volume coefficients. As special cases, we find…

We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to…

We construct a series of conformally invariant differential operators acting on weighted trace-free symmetric 2-tensors by a method similar to Graham-Jenne-Mason-Sparling's. For compact conformal manifolds of dimension even and greater than…

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.

We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfunctions in the kernel of GJMS operators.…

We investigate the prescribed Q-curvature flow for GJMS operators with non-trivial kernel on compact manifolds of even dimension. When the total Q-curvature is negative, we identify a conformally invariant condition on the nodal domains of…

We consider the volume expansion of the Blaschke metric, which is a projectively invariant metric on a strictly convex domain in a locally flat projective manifold. When the boundary is even dimensional, we express the logarithmic…

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 differential operators have leading part a power of the Laplacian.…

For any hypersurface $M$ of a Riemannian manifold $X$, recent works introduced the notions of extrinsic conformal Laplacians and extrinsic $Q$-curvatures. Here we derive explicit formulas for the extrinsic version ${\bf P}_4$ of the Paneitz…

We present an intrinsic Klotz-Osserman type theorem for surfaces in terms of Codazzi operators. Additionally, utilizing Simons' formula, we investigate surfaces with parallel mean curvature with non-positive Gaussian curvature in product…

There is a class of Laplacian like conformally invariant differential operators on differential forms $L^\ell_k$ which may be considered the generalisation to differential forms of the conformally invariant powers of the Laplacian known as…

For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe…

On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the…

For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian…

On an even conformal manifold $(M,c)$, such that the critical GJMS operator has non-trivial kernel, we identify and discuss the role of a finite dimensional vector space $N(Q)$ of functions determined by the conformal structure. Using these…

We construct $Q$-curvature operators on $d$-closed $(1,1)$-forms and on $\overline{\partial}_b$-closed $(0,1)$-forms on five-dimensional pseudohermitian manifolds. These closely related operators give rise to a new formula for the scalar…

This paper derives an explicit formula for Branson's Q-curvature in even-dimensional conformal geometry. The ingredients in the formula come from the Poincare metric in one higher dimension; hence the formula is called holographic. When…

We clarify the conformal invariance of the Pontrjagin forms by giving them a manifestly conformally invariant construction; they are shown to be the Pontrjagin forms of the conformally invariant tractor connection. The Q-curvature is…

We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formul{\ae} for…