Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold
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Let (M, g) be a Riemannian manifold of dimension n≥ 3 and ĝanother metric on M which is pointwise conformai to g. It can be written where u is a positive smooth function on M. Then the curvature of g is computable in terms of that of g and the derivatives of u up to second order. In particular, if S and S denote the scalar curvature of g and g respectively, they are related by the equationwhere ▽u denotes the Laplacian of u, defined with respect to the metric g.
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2019 ◽
Vol 21
(03)
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pp. 1850021
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2005 ◽
Vol 15
(4)
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pp. 589-606
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2007 ◽
Vol 107
(15)
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pp. 3236-3249
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1994 ◽
Vol 311
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pp. 305-324
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