Abstract
Existence, uniqueness and weighted regularity of solutions of linear and nonlinear second-order uniformly elliptic differential equations on complete punctured compact N-manifolds, N > 2. Application to prescribed curvature problems: scalar curvature in a quasi-isometry class (including a contribution to the Lichnérowicz-York equation of General Relativity); Ricci curvature in a weighted Kähler class (with a related result in equiaffine geometry). A new asymptonic behaviour is allowed throughout, called partial decay, which requires its own maximum principle.
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Current support: CNRS; partial support; CEE contract GADGET # SC1-0105-C.
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Delanoe, P. Partial decay on simple manifolds. Ann Glob Anal Geom 10, 3–61 (1992). https://doi.org/10.1007/BF00128337
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DOI: https://doi.org/10.1007/BF00128337
Key words
- punctured compact manifolds
- uniform ellipticity
- asymptotic behaviour
- a priori estimates
- scalar curvature
- Ricci curvature