Journal article

Properties of hypersurface singular sets of solutions to the σk-Yamabe equation in the negative cone

Abstract:: We consider conformally flat Lipschitz viscosity solutions to the σ_k-Yamabe equation in the negative cone which admit smooth hypersurface singularities. Under natural regularity assumptions (that are satisfied by solutions to the σ_k-Loewner-Nirenberg problem on annuli, for example), we first prove that the trace and normal derivatives of such a solution along the hypersurface satisfy a certain PDE. For k = 2, we also show that the hypersurface is minimal with respect to the Lipschitz solution and address some questions related to the formal expansion of the solution near the hypersurface.

Publication status:: Accepted

Peer review status:: Peer reviewed

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APA Style

Duncan, J., & Nguyen, L. (2026). Properties of hypersurface singular sets of solutions to the σk-Yamabe equation in the negative cone. Discrete & Continuous Dynamical Systems.

MLA Style

Duncan, JAJ, and L. Nguyen. “Properties of Hypersurface Singular Sets of Solutions to the Σk-Yamabe Equation in the Negative Cone.” Discrete & Continuous Dynamical Systems, 2026.

Chicago Style

Duncan, JAJ, and L. Nguyen. 2026. “Properties of Hypersurface Singular Sets of Solutions to the Σk-Yamabe Equation in the Negative Cone.” Discrete & Continuous Dynamical Systems.
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Authors

+ Duncan, JAJ More by this author

Role:: Author

+ Nguyen, L More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Oxford college:: St Edmund Hall
Role:: Author
ORCID:: 0000-0002-1364-4433

+ Engineering and Physical Sciences Research Council More from this funder

Funder identifier:: https://ror.org/0439y7842
Grant:: EP/V521917/1

Publisher:: American Institute of Mathematical Sciences
Journal:: Discrete & Continuous Dynamical Systems More from this journal
Acceptance date:: 2026-10-25
EISSN:: 1553-5231
ISSN:: 1078-0947

Language:: English
Pubs id:: 2489945
Local pid:: pubs:2489945
Deposit date:: 2026-10-29
ARK identifier:: ark:/29072/ora_b1389f41e7f540f4841883ffdcaf9ec6

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