Characterizations of the compactness of Riemannian manifolds by eigenfunctions, and a partial proof of a conjecture by Hamilton (Q309467)
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scientific article; zbMATH DE number 6624470
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterizations of the compactness of Riemannian manifolds by eigenfunctions, and a partial proof of a conjecture by Hamilton |
scientific article; zbMATH DE number 6624470 |
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Characterizations of the compactness of Riemannian manifolds by eigenfunctions, and a partial proof of a conjecture by Hamilton (English)
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7 September 2016
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The author establishes comparison theorems related to the first eigenvalue of the Schrödinger operator. On the basis of these results, characterizations of Ricci solitons as space forms are obtained. Partial answer to a conjecture formulated by Hamilton is given.
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Laplacian operator
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Schrödinger operator
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eigenvalue
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Dirichlet eigenvalue
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eigenfunction
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0.90616715
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0.89863527
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0.8950988
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