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Electronic Research Announcements in Mathematical Sciences (ERA-MS)
 

Scalar curvature and $Q$-curvature of random metrics

Pages: 43 - 56, Volume 17, 2010      doi:10.3934/era.2010.17.43

 
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Yaiza Canzani - Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Str. West, Montréal QC H3A 2K6, Canada (email)
Dmitry Jakobson - Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Str. West, Montréal QC H3A 2K6, Canada (email)
Igor Wigman - Centre de recherches mathématiques (CRM), Université de Montréal C.P. 6128, succ. centre-ville Montréal, Québec H3C 3J7, Canada (email)

Abstract: We study Gauss curvature for random Riemannian metrics on a compact surface, lying in a fixed conformal class; our questions are motivated by comparison geometry. We next consider analogous questions for the scalar curvature in dimension $n>2$, and for the $Q$-curvature of random Riemannian metrics.

Keywords:  Comparison geometry, conformal class, scalar curvature, $Q$-curvature, Gaussian random fields, excursion probability, Laplacian, conformally covariant operators.
Mathematics Subject Classification:  Primary: 60G60; Secondary: 53A30, 53C21, 58J50, 58D17, 58D20.

Received: January 2010;      Revised: June 2010;      Available Online: July 2010.