Existence and uniqueness of Green's functions to nonlinear Yamabe problems
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 fl...
| Κύριοι συγγραφείς: | , |
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| Μορφή: | Journal article |
| Γλώσσα: | English |
| Έκδοση: |
Wiley
2022
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| _version_ | 1826310594862514176 |
|---|---|
| author | Li, Y Nguyen, LUC |
| author_facet | Li, Y Nguyen, LUC |
| author_sort | Li, Y |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:55:42Z |
| format | Journal article |
| id | oxford-uuid:38bf4d47-4774-4100-9ccc-1745ac25c6eb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:55:42Z |
| publishDate | 2022 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:38bf4d47-4774-4100-9ccc-1745ac25c6eb2023-08-17T07:57:48ZExistence and uniqueness of Green's functions to nonlinear Yamabe problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:38bf4d47-4774-4100-9ccc-1745ac25c6ebEnglishSymplectic ElementsWiley2022Li, YNguyen, LUCFor 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. |
| spellingShingle | Li, Y Nguyen, LUC Existence and uniqueness of Green's functions to nonlinear Yamabe problems |
| title | Existence and uniqueness of Green's functions to nonlinear Yamabe problems |
| title_full | Existence and uniqueness of Green's functions to nonlinear Yamabe problems |
| title_fullStr | Existence and uniqueness of Green's functions to nonlinear Yamabe problems |
| title_full_unstemmed | Existence and uniqueness of Green's functions to nonlinear Yamabe problems |
| title_short | Existence and uniqueness of Green's functions to nonlinear Yamabe problems |
| title_sort | existence and uniqueness of green s functions to nonlinear yamabe problems |
| work_keys_str_mv | AT liy existenceanduniquenessofgreensfunctionstononlinearyamabeproblems AT nguyenluc existenceanduniquenessofgreensfunctionstononlinearyamabeproblems |