Compactness of solutions to the Yamabe problem. III

2006/12/12 by Yanyan Li, Lei Zhang, Li, YanYan +1 · 4 citations
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0612297

Abstract

For a sequence of blow up solutions of the Yamabe equation on non-locally confonformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds.

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