Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds. (English) Zbl 0645.53023

Investigating the solution of the Monge-Ampère equation the author proves that \(\hat M=M\setminus \Gamma\) admits a complete metric \(\hat g\) conformally equivalent to g in case \((M^ n,g)\) is a compact Riemannian manifold and \(\Gamma\) is a closed smooth submanifold of dimension \(d>n- 2/2\).
Reviewer: Th.Friedrich


53C20 Global Riemannian geometry, including pinching
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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