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Weighted L2 Holomorphic Functions on Ball-Fiber Bundles Over Compact Kähler Manifolds

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Title
Weighted L2 Holomorphic Functions on Ball-Fiber Bundles Over Compact Kähler Manifolds
Author(s)
Seungjae Lee; Seo, Aeryeong
Publication Date
2023-07
Journal
Journal of Geometric Analysis, v.33, no.7
Publisher
Springer
Abstract
Let M~ be a complex manifold, Γ be a torsion-free cocompact lattice of Aut (M~) and ρ: Γ → SU(N, 1) be a representation. Suppose that there exists a ρ -equivariant totally geodesic isometric holomorphic embedding (Formula presented.). In this paper, we investigate a relation between weighted L2 holomorphic functions on the fiber bundle Ω : = M× ρBN and the holomorphic sections of the pull-back bundle ı∗(SmTΣ∗) over M. In particular, Aα2(Ω) has infinite dimension for any α> - 1 and if n< N , then A-12(Ω) also has the same property. As an application, if Γ is a torsion-free cocompact lattice in (Formula presented.), and (Formula presented.) is a maximal representation, then for any α> - 1 , Aα2(Bn×ρBN) has infinite dimension. If n< N , then A-12(Bn×ρBN) also has the same property. © 2023, Mathematica Josephina, Inc.
URI
https://pr.ibs.re.kr/handle/8788114/14351
DOI
10.1007/s12220-023-01288-9
ISSN
1050-6926
Appears in Collections:
Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
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