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Abstract
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We consider the prescribed scalar curvature equation on an open set
of ,
with
(), and we prove
the inequality
where
is a
compact set of
.
In dimension 4, we have an idea on the supremum of the solution of the prescribed
scalar curvature if we control the infimum. For this case we suppose the scalar curvature
().
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Keywords
$\sup \times \inf$, nonlinear perturbation, dimension 4,
minimal conditions
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Mathematical Subject Classification 2010
Primary: 35B44, 35B45, 35B50, 35J60, 53C21
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Milestones
Received: 7 November 2017
Revised: 24 October 2018
Accepted: 2 November 2018
Published: 16 September 2019
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