In this talk we will discuss the existence and compactness of positive solutions to a family of semi-linear conformally invariant equations. The family of conformally covariant operators were introduced via the scattering theory for Poincare metrics associated with a conformal manifold. We will show that, on a closed and locally conformally flat manifold with Poincare exponent small, the set of positive smooth solutions to the family of equations is compact in the C^infty topology. Therefore the existence of positive solutions follows from the existence of Yamabe metrics and a degree theory.

Lecture #12232

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