Fu-Zhou Gong, Feng-Yu Wang, "On Gromov's theorem and -Hodge decomposition", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 650181, 20 pages, 2004. https://doi.org/10.1155/S0161171204210365
On Gromov's theorem and -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 -harmonic sections. In particular, some known results concerning Gromov's theorem and the -Hodge decomposition are considerably improved.
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