The fully nonlinear Loewner-Nirenberg problem is shown to admit solutions when mu_Gamma^+>1-delta, in particular for sigma_k with k<=n/2, and whenever any admissible conformal metric exists.
A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary
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In this paper we establish existence and compactness of solutions to a general fully nonlinear version of the Yamabe problem on locally conformally flat Riemannian manifolds with umbilic boundary.
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The $\sigma_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k=\frac{n}{2}$ and beyond
The fully nonlinear Loewner-Nirenberg problem is shown to admit solutions when mu_Gamma^+>1-delta, in particular for sigma_k with k<=n/2, and whenever any admissible conformal metric exists.