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Dirac and Plateau billiards in domains with corners

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Gromov M.

Open Mathematics

2014

tom 12

nr 8

1109-1156

Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below.

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1 Open Mathematics

1 Gromov M.

1 2014

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Dirac and Plateau billiards in domains with corners