Abstract
We study the conformal deformation for prescribing scalar curvature function\(\bar S\) on Cartan-Hadamard manifoldMn(n≥3) with strongly negative curvature. By employing the supersubsolution method and a careful construction for the supersolution, we obtain the best possible asymptotic behavior for\(\bar S\) near infinity so that the problem of complete conformal deformation is solvable. In more general cases, we prove an asymptotic estimation on the solutions of the conformal scalar curvature equation.
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