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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832566741625995264 |
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| author | Fu-Zhou Gong Feng-Yu Wang |
| author_facet | Fu-Zhou Gong Feng-Yu Wang |
| author_sort | Fu-Zhou Gong |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-2521c68ba7854b02aa79447dda248ceb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2521c68ba7854b02aa79447dda248ceb2025-02-03T01:03:14ZengWileyInternational 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 |
| spellingShingle | Fu-Zhou Gong Feng-Yu Wang On Gromov's theorem and L 2-Hodge decomposition International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | On Gromov's theorem and L 2-Hodge decomposition |
| title_sort | on gromov s theorem and l 2 hodge decomposition |
| url | http://dx.doi.org/10.1155/S0161171204210365 |
| work_keys_str_mv | AT fuzhougong ongromovstheoremandl2hodgedecomposition AT fengyuwang ongromovstheoremandl2hodgedecomposition |