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Infinite-Dimensionality of Bergman Spaces on\ Complete d-Bounded Kähler Manifolds
Abstract
Let M be a complete Kähler manifold of complex dimension n≥ 1 whose Kähler form is d-bounded in the sense of Gromov. We prove that its Bergman space, namely the Hilbert space of L2 holomorphic n-forms, is infinite-dimensional. The proof combines Gromov's construction of auxiliary holomorphic line bundles, parameter-uniform db estimates, and L2 methods with singular weights.
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BibTeX
@misc{chen2026infinitedimensionality,
title = {{Infinite-Dimensionality of Bergman Spaces on\ Complete $d$-Bounded Kähler Manifolds}},
author = {Bo-Yong Chen and Jujie Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05205},
eprint = {2610.05205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05205},
}
RIS
TY - UNPB
TI - Infinite-Dimensionality of Bergman Spaces on\ Complete d-Bounded Kähler Manifolds
AU - Bo-Yong Chen
AU - Jujie Wu
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05205
UR - https://arxiv.org/abs/2610.05205
AB - Let M be a complete Kähler manifold of complex dimension n≥ 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.
ER -