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Conformal metrics with prescribed curvature functions on manifolds with boundary
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 4, August 2007
- pp. 915-942
- 10.1353/ajm.2007.0025
- Article
- Additional Information
We study the Dirichlet problem for a class of fully nonlinear elliptic equations related to conformal deformations of metrics on Riemannian manifolds with boundary. As a consequence we prove the existence of a conformal metric, given its value on the boundary as a prescribed metric conformal to the (induced) background metric, with a prescribed curvature function of the Schouten tensor.