An extension of prescribed problems on the conformal classes of complete metrics

Abstract

We solve prescribed problems for modified Schouten tensors in the conformal classes of smooth complete metrics, which extends the results obtained in prequel \cite{yuan-PUE1}. The key ingredient is to confirm the uniform ellipticity of operators under an assumption, which is sharp as shown by obstructions from topology and function theory.

arXiv commentSections 4 and 5 added, Typos fixed, References updated