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Constant Scalar Curvature Metrics on Connected Sums

Abstract:

The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension $n \geq 3$, which minimizes the total scalar curvature of this conformal class. Let $(M',g')$ and $(M'',g'')$ be compact Riemannian $n$-manifolds. We form their connected sum $M'\#M''$ by removing small balls of radius $\epsilon$ from $M'$, $M''$ and gluing together the $S^{n-1}$ boundaries, and make a metric $g...

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Dominic Joyce More by this author
Publication date:
2003
URN:
uuid:32ee7884-20ee-4247-ae32-ec38d6112d3c
Local pid:
oai:eprints.maths.ox.ac.uk:78

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