Dirac and Plateau billiards in domains with corners

• Autorzy: Misha Gromov
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Scalar curvature; Dirac operator; Plateau problem; Reflection groups

Kategorie tematyczne

• 53C23: Global geometric and topological methods (\`a la Gromov); differential geometric analysis on metric spaces
• 53C20: Global Riemannian geometry, including pinching
• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 53A05: Surfaces in Euclidean space
• 53A10: Minimal surfaces, surfaces with prescribed mean curvature
• 53C40: Global submanifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 8
• Strony: 1109-1156

Daty

wydano

2014-08-01

online

2014-05-08

Twórcy

autor

Misha Gromov

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Identyfikatory

DOI

10.2478/s11533-013-0399-1