International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 1, Pages 25-44
On Gromov's theorem and -Hodge decomposition
1Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
2Department of Mathematics, Beijing Normal University, Beijing 100875, China
Received 22 October 2002
Copyright © 2004 Fu-Zhou Gong and Feng-Yu Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 -harmonic sections. In particular, some known results concerning Gromov's theorem and the -Hodge decomposition are considerably improved.