Infinite-Dimensionality of Bergman Spaces on\ Complete $d$-Bounded Kähler Manifolds

Bo-Yong Chen; Jujie Wu

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arXiv · 2610.05205

Infinite-Dimensionality of Bergman Spaces on\ Complete $d$-Bounded Kähler Manifolds

Bo-Yong Chen·Jujie Wu

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Abstract

Let $M$ be a complete Kähler manifold of complex dimension $n\geq 1$ whose Kähler form is $d$-bounded in the sense of Gromov. We prove that its Bergman space, namely the Hilbert space of $L^2$ holomorphic $n$-forms, is infinite-dimensional. The proof combines Gromov's construction of auxiliary holomorphic line bundles, parameter-uniform $\db$ estimates, and $L^2$ methods with singular weights.

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BibTeX RIS

Bo-Yong Chen, Jujie Wu. 2026-10-04. Infinite-Dimensionality of Bergman Spaces on\ Complete $d$-Bounded Kähler Manifolds. https://arxiv.org/abs/2610.05205

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