A finiteness theorem for ends of complete manifolds supporting a Sobolev type inequality (Q540466)
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scientific article; zbMATH DE number 5903720
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A finiteness theorem for ends of complete manifolds supporting a Sobolev type inequality |
scientific article; zbMATH DE number 5903720 |
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A finiteness theorem for ends of complete manifolds supporting a Sobolev type inequality (English)
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3 June 2011
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The author proves a finite ends and a one end theorem for complete, non-compact Riemannian manifolds supporting a Sobolev-type inequality. The results are achieved using the theory of harmonic functions. In particular, the author states a result which strengthens a similar kind of theorem proved by \textit{G. Tian} and \textit{J. Viaclovsky} in [Comment. Math. Helv. 83, No. 4, 889--911 (2008; Zbl 1154.53024)]. Several known results are derived, also.
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complete manifolds
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finite end theorem
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Sobolev inequality
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