The Yamabe equation on complete manifolds with finite volume

Details The Yamabe equation on complete manifolds with finite volume The Yamabe equation on complete manifolds with finite volume

2011-11-10

arxiv.org/abs/1111.2471v1

Mathematics

Differential Geometry

Scientific paper

We prove the existence of a solution of the Yamabe equation on complete manifolds with finite volume and positive Yamabe invariant. In order to circumvent the standard methods on closed manifolds which heavily rely on global (compact) Sobolev embeddings we approximate the solution by eigenfunctions of certain conformal complete metrics. This also gives rise to a new proof of the well-known result for closed manifolds and positive Yamabe invariant.

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