Scalar curvature on any closed even-dimensional manifold with nonzero Euler characteristic can be increased by at most an explicit constant, the gap, which is a function of the minimal eigenvalue of the curvature operator of the starting metric.
Rigid ity of spin fill-ins with non-negative scalar curvature
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Gap phenomenon for scalar curvature
Scalar curvature on any closed even-dimensional manifold with nonzero Euler characteristic can be increased by at most an explicit constant, the gap, which is a function of the minimal eigenvalue of the curvature operator of the starting metric.