The Q curvature is a curvature quantity on even dimensional manifolds that yields a prescription problem which, in terms of elementary geometric analysis, is a higher-dimensional generalisation of the 2-dimensional Gauss curvature prescription problem. I will give a proof that Q is constant on Einstein manifolds. Closely related to Q curvature is a family of higher order conformal Laplacians due to Graham-Jenne-Mason-Sparling (GJMS). I will show that on Einstein manifolds these factor into a composition of second order Laplacian type operators and show that the GJMS family of operators may be extended in this setting.

Lecture #12239

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