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• W2786572364 abstract "For the bundle-valued differential forms on complex manifolds, a method of solving $$bar {partial }$$ -equations with a control of L 2 norm is discussed. Basic results are existence theorems for such solutions under curvature conditions. They are variants of Kodaira’s cohomology vanishing theorem on compact Kähler manifolds, and formulated as vanishing theorems with L 2 conditions. Some of these L 2 vanishing theorems are generalized to finite-dimensionality theorems under the assumptions on the bundle-convexity. Besides applications to holomorphic functions, extensions of the Hodge theory to noncompact manifolds will also be discussed." @default.
• W2786572364 created "2018-02-23" @default.
• W2786572364 creator A5072945209 @default.
• W2786572364 date "2018-01-01" @default.
• W2786572364 modified "2023-09-27" @default.
• W2786572364 title "Analyzing the L 2 ∂ ̄ $$L{{ }^2} bar {partial }$$ -Cohomology" @default.
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• W2786572364 doi "https://doi.org/10.1007/978-4-431-56852-0_2" @default.
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