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Partial decay on simple manifolds

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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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  1. Université de Nice-Sophia Antipolis, .I.M.S.P. Parc Valrose, F-06034, Nice Cedex

    Philippe Delanoe

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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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