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Scalar Curvature Gap Estimates and Epsilon-Gap Distance Extremality

A twisted-Dirac index-theory estimate bounding how much an area-nonincreasing map of nonzero degree can raise scalar curvature, with no sign assumption on the target's curvature operator, showing every metric on an even-dimensional closed manifold with nonzero Euler characteristic is epsilon-gap distance extremal for some epsilon>=0, plus a boundary analogue for scalar and mean curvature.

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GAP PHENOMENON FOR SCALAR CURVATURE YUKAI SUN AND CHANGLIANG WANG Abstract. Inspired by

Derives an upper bound on the infimum of scalar curvature for area-nonincreasing maps of nonzero degree between even-dimensional spin manifolds, without assuming the target's curvature operator is no…