Resumen de Origins, Applications and Generalisations of the Q -Curvature

Thomas B. Branson, A. Rod Gover

• These expository notes sketch the origins of Branson�s Q-curvature. We give an introductory account of the equations governing its prescription, its roles in a conformal action formula as well as in Polyakov-type formulae for the conformal variation of the functional determinants of suitable elliptic operators. We indicate how properties, which partly characterise the Q-curvature, identify it as an extreme case of a class of differential operators on closed differential forms; these so-called Q-operators generalise the Q-curvature.