Schouten tensor equations in conformal geometry with prescribed boundary metric
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We 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.
CitationSchnürer, O. C. (2005). Schouten tensor equations in conformal geometry with prescribed boundary metric. Electronic Journal of Differential Equations, 2005(81), pp. 1-17.
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