Every Riemannian metric with scalar curvature at least κ on a closed manifold, or on an open manifold when κ≤0, is a local Burnett-class limit of metrics with scalar curvature exactly κ, with sharp Hölder closures.
Almost prescribing scalar curvature by mixed convex integration
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abstract
We introduce a method of mixed convex integration and demonstrate its suitability for solving a particular class of semilinear second-order partial differential relations. As an application, we provide a new proof of a result on scalar curvature originally established by Lohkamp.
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Scalar Curvature Flexibility in the Riemannian Burnett Compactness Class
Every Riemannian metric with scalar curvature at least κ on a closed manifold, or on an open manifold when κ≤0, is a local Burnett-class limit of metrics with scalar curvature exactly κ, with sharp Hölder closures.