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Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold
Published online by Cambridge University Press: 22 January 2016
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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 equation
where ▽u denotes the Laplacian of u, defined with respect to the metric g.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1993
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