An obstruction to the conformal compactification of Riemannian manifolds

Kim, Seongtag

doi:10.1090/S0002-9939-99-05207-7

An obstruction to the conformal compactification of Riemannian manifolds
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Proc. Amer. Math. Soc. 128 (2000), 1833-1838 Request permission

Abstract:

In this paper, we study noncompact complete Riemannian $n$-manifolds with $n\ge 3$ which are not pointwise conformal to subdomains of any compact Riemannian $n$-manifold. For this, we compare the Sobolev Quotient at infinity of a noncompact complete Riemannian manifold with that of the singular set in a compact Riemannian manifold using the method for the Yamabe problem.

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