Dirac and Plateau billiards in domains with corners

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• 作者：Misha Gromov (1) (2)
  
• 关键词：53A05 ; 53A10 ; 53C20 ; 53C21 ; 53C23 ; 53C40 ; Scalar curvature ; Dirac operator ; Plateau problem ; Reflection groups
• 刊名：Central European Journal of Mathematics
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：12
• 期：8
• 页码：1109-1156
• 全文大小：
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• 作者单位：Misha Gromov (1) (2)
  
  1. Institut des Hautes ètudes Scientifiques, Route de Chartres 35, 91440, Bures-sur-Yvette, France
  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY, 10012, USA
  
• ISSN：1644-3616

文摘

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 scal g (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.