摘要
We consider the problem of finding on a given Euclidean domainof dimension n≥3 a complete conformally flat metric whose Schouten curvature A satisfies some equations of the form f(λ(−A))=1.This generalizes a problem considered by Loewner and Nirenberg for the scalar curvature.We prove the existence and uniqueness of such metric when the boundary δΩ is a smooth bounded hypersurface(of codimension one).When δΩ contains a compact smooth submanifold ∑ of higher codimension with δΩ\∑ being compact,we also give a‘sharp’condition for the divergence to infinity of the conformal factor near ∑ in terms of the codimension.
基金
supported by Spanish government Grants MTM2014-52402-C3-1-P and MTM2017-85757-P
the BBVA Foundation Grant for Researchers and Cultural Creators 2016
supported by NSF Grant DMS-1501004.
