Scalar and mean curvature comparison via the Dirac operator

• DOI: 10.2140/gt.2024.28.1167
• Publication Date: 2024-05-16T12:32:10Z
• Authors: Simone Cecchini; Rudolf Zeidler
• Keywords: Manifold (fluid mechanics); Operator (biology)

We use the Dirac operator technique to establish sharp distance estimates for compact spin manifolds under lower bounds on scalar curvature in interior and mean of boundary.In situations we consider, thereby give refined answers questions metric inequalities recently proposed by Gromov.This includes optimal Riemannian bands long neck problem.In case over non-vanishing A-genus, a rigidity result stating that any band attaining predicted upper bound is isometric particular warped product some manifold admitting parallel spinor.Furthermore, scalar-and extremality results certain log-concave products.The latter annuli all simply-connected space forms.On technical level, our proofs are based new spectral augmented Lipschitz potential together with local boundary conditions.