Advances in Pure Mathematics

Volume 1, Issue 2 (March 2011)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

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The Harmonic Functions on a Complete Asymptotic Flat Riemannian Manifold

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DOI: 10.4236/apm.2011.12003    4,524 Downloads   11,008 Views  
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ABSTRACT

Let be a simply connected complete Riemannian manifold with dimension n≥3 . Suppose that the sectional curvature satisfies , where p is distance function from a base point of M, a, b are constants and . Then there exist harmonic functions on M .

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H. Zhan, "The Harmonic Functions on a Complete Asymptotic Flat Riemannian Manifold," Advances in Pure Mathematics, Vol. 1 No. 2, 2011, pp. 5-8. doi: 10.4236/apm.2011.12003.

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