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Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry

Abstract:
We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is $C^{1,1}$. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by $C^{1,1}$ solutions on larger and larger compact domains, and, in particular, for entire $C^{1,1}_{\rm loc}$ solutions: they are either constants or standard bubbles.
Publication status:
Accepted
Peer review status:
Reviewed (other)

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Edmund Hall
Role:
Author

Contributors

Role:
Editor
Role:
Editor
Role:
Editor
Role:
Editor
Publisher:
Springer Publisher's website
Series:
Progress in Mathematics
Host title:
Geometric Analysis: In Honor of Gang Tian's 60th Birthday
Publication date:
2019-01-01
Source identifiers:
1004696
Keywords:
Pubs id:
pubs:1004696
UUID:
uuid:7bd8bd41-f39b-4cb7-af6f-af3827041c14
Local pid:
pubs:1004696
Deposit date:
2019-06-01

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