Constant scalar curvature metrics with isolated singularities

Details Constant scalar curvature metrics with isolated singularities Constant scalar curvature metrics with isolated singularities

1996-05-14

arxiv.org/abs/dg-ga/9605004v1

Mathematics

Differential Geometry

Latex2e, 48 pages

Scientific paper

We extend the results and methods of \cite{MP} to prove the existence of constant positive scalar curvature metrics $g$ which are complete and conformal to the standard metric on $S^N \setminus \Lambda$, where $\Lambda$ is a disjoint union of submanifolds of dimensions between 0 and $(N-2)/2$. The existence of solutions with isolated singularities occupies the majority of the paper; their existence was previously established by Schoen \cite{S}, but the proof we give here, based on the techniques of \cite{MP}, is more direct, and provides more information about their geometry. When $\Lambda$ is discrete we also establish that these solutions are smooth points in the moduli spaces of all such solutions introduced and studied in \cite{MPU1} and \cite{MPU2}

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