Dirac and Plateau billiards in domains with corners

Misha Gromov

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1109-1156
Number of pages48
JournalCentral European Journal of Mathematics
Volume12
Issue number8
DOIs
StatePublished - Aug 2014

Keywords

  • Dirac operator
  • Plateau problem
  • Reflection groups
  • Scalar curvature

ASJC Scopus subject areas

  • Mathematics(all)

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