Journal article
Existence and uniqueness of Green's functions to nonlinear Yamabe problems
- Abstract:
- For a given finite subset S of a compact Riemannian manifold (M, g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M \ S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the conformal metric belongs to the boundary of the given cone. As a by-product, we define a purely local notion of Ricci lower bounds for continuous metrics which are conformal to smooth metrics and prove a corresponding volume comparison theorem.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.5MB, Terms of use)
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- Publisher copy:
- 10.1002/cpa.22044
Authors
- Publisher:
- Wiley
- Journal:
- Communications on Pure and Applied Mathematics More from this journal
- Volume:
- 76
- Issue:
- 8
- Pages:
- 1554-1607
- Publication date:
- 2022-03-10
- Acceptance date:
- 2021-02-08
- DOI:
- EISSN:
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1097-0312
- ISSN:
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0010-3640
- Language:
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English
- Keywords:
- Pubs id:
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1161990
- Local pid:
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pubs:1161990
- Deposit date:
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2021-02-17
- ARK identifier:
Terms of use
- Copyright holder:
- Li and Nguyen
- Copyright date:
- 2022
- Rights statement:
- © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
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