Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Complete conformal metrics with zero scalar curvature


Authors: Xiaoyun Ma and Robert C. McOwen
Journal: Proc. Amer. Math. Soc. 115 (1992), 69-77
MSC: Primary 53C21; Secondary 35B40, 58G30
MathSciNet review: 1101988
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider the problem of when a noncompact Riemannian manifold $ \widehat{M}$ admits a complete conformal metric with zero scalar curvature. In particular, we show that this can be achieved if $ \widehat{M}$ is the noncompact manifold obtained by deleting a smooth submanifold $ {\Gamma ^n}$ from a compact Riemannian manifold $ {M^N}$ provided $ n \leq (N - 2)/2$ and the Sobolev quotient is positive.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C21, 35B40, 58G30

Retrieve articles in all journals with MSC: 53C21, 35B40, 58G30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1101988-1
PII: S 0002-9939(1992)1101988-1
Keywords: Conformal metrics, conformal Laplacian, scalar curvature, Riemannian manifolds
Article copyright: © Copyright 1992 American Mathematical Society