Electron. J. Diff. Eqns., Vol. 2005(2005), No. 81, pp. 1-17.

Schouten tensor equations in conformal geometry with prescribed boundary metric

Oliver C. Schnuerer

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.

Submitted March 15, 2004. Published July 15, 2005.
Math Subject Classifications: 53A30; 35J25; 58J32.
Key Words: Schouten tensor; fully nonlinear equation; conformal geometry; Dirichlet boundary value problem.

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Oliver C. Schnüurer
Freie Universität Berlin
Arnimallee 2-6, 14195 Berlin, Germany
email: Oliver.Schnuerer@math.fu-berlin.de

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