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...
| Autores principales: | , |
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| Formato: | Journal article |
| Lenguaje: | English |
| Publicado: |
Wiley
2022
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| Sumario: | 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. |
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