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arXiv · 1505.04322

On the growth of von Neumann dimension of harmonic spaces of semipositive line bundles over covering manifolds

Huan Wang
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Abstract

We study the harmonic space of line bundle valued forms over a covering manifold with a discrete group action $\Gamma$, and obtain an asymptotic estimate for the $\Gamma$-dimension of the harmonic space with respect to the tensor times $k$ in the holomorphic line bundle $L^{k}\otimes E$ and the type $(n,q)$ of the differential form, when $L$ is semipositive. In particular, we estimate the $\Gamma$-dimension of the corresponding reduced $L^2$-Dolbeault cohomology group. Essentially, we obtain a local estimate of the pointwise norm of harmonic forms with valued in semipositive line bundles over Hermitian manifolds.

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Huan Wang. 2015-05-16. On the growth of von Neumann dimension of harmonic spaces of semipositive line bundles over covering manifolds. https://doi.org/10.1142/s0129167x16500932

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