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The axisymmetric σk-Nirenberg problem

Abstract:

We study the problem of prescribing $\sigma_k$-curvature for a conformal metric on the standard sphere $\mathbb{S}^n$ with $2 \leq k < n/2$ and $n \geq 5$ in axisymmetry. Compactness, non-compactness, existence and non-existence results are proved in terms of the behaviors of the prescribed curvature function $K$ near the north and the south poles. For example, consider the case when the north and the south poles are local maximum points of $K$ of flatness order $\beta \in [2,n)$. We prove...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jfa.2021.109198

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Edmund Hall
Role:
Author
ORCID:
0000-0002-1364-4433
Publisher:
Elsevier Publisher's website
Journal:
Journal of Functional Analysis Journal website
Volume:
281
Issue:
9
Article number:
109198
Publication date:
2021-07-16
Acceptance date:
2021-07-09
DOI:
ISSN:
0022-1236
Language:
English
Keywords:
Pubs id:
1183071
Local pid:
pubs:1183071
Deposit date:
2021-06-25

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