# Journal article

## Existence and uniqueness to a fully nonlinear version of the Loewner–Nirenberg problem: Dedicated to celebrate the sixtieth anniversary of USTC

Abstract:

We consider the problem of finding on a given Euclidean domain Ω of 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 ∂Ω is a smooth bounded hypersurface (of codimension one). When ∂Ω contains a compact smooth submanifold Σ of higher codimension...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Accepted manuscript, pdf, 353.6KB)
Publisher copy:
10.1007/s40304-018-0150-0

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Edmund Hall
Role:
Author
Publisher:
Springer Berlin Heidelberg Publisher's website
Journal:
Communications in Mathematics and Statistics Journal website
Volume:
6
Issue:
3
Pages:
269–288
Publication date:
2018-08-25
Acceptance date:
2018-06-21
DOI:
EISSN:
2194-671X
ISSN:
2194-6701
Keywords:
Pubs id:
pubs:858717
UUID:
uuid:3da71d47-3461-49ad-b02c-de8f0d860d1d
Local pid:
pubs:858717
Source identifiers:
858717
Deposit date:
2018-06-21

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