International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 1-4, Pages 25-44
doi:10.1155/S0161171204210365
On Gromov's theorem and L 2-Hodge decomposition
Fu-Zhou Gong1
and Feng-Yu Wang2
1Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
2Department of Mathematics, Beijing Normal University, Beijing 100875, China
Abstract
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.