Yamabe type problems and their applications (A07)

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Motivated by the Yamabe problem, we want to find a "good" or "best" metric in a conformal class or in a transversal conformal class. Here by a good metric in a conformal class we mean a conformal metric with constant 2-scalar curvature, while by a good metric in a transversal conformal metric we mean a transversal metric with constant transversal metric. The first problem involves a fully nonlinear equation and the second a critical transversal elliptic equation.