Existence and Uniqueness to a Fully Nonlinear Version of the Loewner–Nirenberg Problem Dedicated to Celebrate the Sixtieth Anniversary of USTC  

作　　者：María del Mar González YanYan Li Luc Nguyen 

机构地区：[1]Departamento de Matemáticas,Universidad Autónoma de Madrid,Campus de Cantoblanco,28049 Madrid,Spain [2]Department of Mathematics,Hill Center,Busch Campus,Rutgers University,110 Frelinghuysen Road,Piscataway,NJ 08854,USA [3]Mathematical Institute and St Edmund Hall,University of Oxford,Andrew Wiles Building,Radcliffe Observatory Quarter,Woodstock Road,Oxford OX26GG,UK

出　　处：《Communications in Mathematics and Statistics》2018年第3期269-288,共20页数学与统计通讯（英文）

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.

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.

关 键 词：Fully nonlinear Loewner-Nirenberg problem Singular fully nonlinear Yamabe metrics Conformal invariance 

分 类 号：O17[理学—数学]