Schnurer, Oliver C.2021-05-282021-05-282005-07-15Schnürer, O. C. (2005). Schouten tensor equations in conformal geometry with prescribed boundary metric. <i>Electronic Journal of Differential Equations, 2005</i>(81), pp. 1-17.1072-6691https://hdl.handle.net/10877/13682We deform the metric conformally on a manifold with boundary. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior, provided that there exists a subsolution. This problem reduces to a Monge-Ampere equation with gradient terms. The main issue is to obtain a priori estimates for the second derivatives near the boundary.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalSchouten tensorFully nonlinear equationConformal geometryDirichlet boundary value problemArticle