Scalar curvature and$Q$-curvature of random metrics

Yaiza Canzani; Dmitry Jakobson; Igor Wigman

doi:10.3934/era.2010.17.43

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

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Scalar curvature and $Q$-curvature of random metrics

1.
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Str. West, Montréal QC H3A 2K6
2.
Centre de recherches mathématiques (CRM), Université de Montréal C.P. 6128, succ. centre-ville Montréal, Québec H3C 3J7

Received: December 31, 2009

Revised: May 31, 2010

Published: December 2009

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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.

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Mathematics Subject Classification: Primary: 60G60; Secondary: 53A30, 53C21, 58J50, 58D17, 58D20.

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