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Title:
Distance estimates under lower scalar curvature bounds in the spin setting and beyond
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Abstract:
We will discuss several situations in which lower scalar curvature bounds can be used to infer certain distance estimates using the Dirac operator on spin manifolds. This includes Gromov’s question on the distance between the boundary components of „bands“, rigidity properties of warped products, and related questions in the context of Witten’s spinor proof of the positive mass theorem. Finally, we will contrast this with a recently obtained result in the non-spin setting concerning the non-existence of complete psc metrics on certain manifolds which admit a compact incompressible hypersurface without psc. Based on joint works with S. Cecchini and D. Räde.
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