On Gromov's theorem and L 2-Hodge decomposition
Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the corresponding L 2-harmonic sections. In particular, some known results concerning Gro...
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Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204210365 |
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doaj-2521c68ba7854b02aa79447dda248ceb2020-11-24T22:48:56ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-0120041254410.1155/S0161171204210365On Gromov's theorem and L 2-Hodge decompositionFu-Zhou Gong0Feng-Yu Wang1Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, ChinaDepartment of Mathematics, Beijing Normal University, Beijing 100875, ChinaUsing a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the corresponding L 2-harmonic sections. In particular, some known results concerning Gromov's theorem and the L 2-Hodge decomposition are considerably improved.http://dx.doi.org/10.1155/S0161171204210365 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Fu-Zhou Gong Feng-Yu Wang |
| spellingShingle |
Fu-Zhou Gong Feng-Yu Wang On Gromov's theorem and L 2-Hodge decomposition International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Fu-Zhou Gong Feng-Yu Wang |
| author_sort |
Fu-Zhou Gong |
| title |
On Gromov's theorem and L 2-Hodge decomposition |
| title_short |
On Gromov's theorem and L 2-Hodge decomposition |
| title_full |
On Gromov's theorem and L 2-Hodge decomposition |
| title_fullStr |
On Gromov's theorem and L 2-Hodge decomposition |
| title_full_unstemmed |
On Gromov's theorem and L 2-Hodge decomposition |
| title_sort |
on gromov's theorem and l 2-hodge decomposition |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| description |
Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the corresponding L 2-harmonic sections. In particular, some known results concerning Gromov's theorem and the L 2-Hodge decomposition are considerably improved. |
| url |
http://dx.doi.org/10.1155/S0161171204210365 |
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AT fuzhougong ongromovstheoremandl2hodgedecomposition AT fengyuwang ongromovstheoremandl2hodgedecomposition |
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1725677998898675712 |