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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0399-1,
author = {Misha Gromov},
title = {Dirac and Plateau billiards in domains with corners},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1109-1156},
zbl = {1315.53027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0399-1}
}
Misha Gromov. Dirac and Plateau billiards in domains with corners. Open Mathematics, Tome 12 (2014) pp. 1109-1156. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0399-1/
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