Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Vanishing theorems of 𝐿2-cohomology groups on Hessian manifolds
Shinya Akagawa
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2019 Volume 71 Issue 1 Pages 65-89

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Abstract

We show vanishing theorems of 𝐿2-cohomology groups of Kodaira–Nakano type on complete Hessian manifolds by introducing a new operator ∂'𝐹. We obtain further vanishing theorems of 𝐿2-cohomology groups $𝐿^2 𝐻^{𝑝,𝑞}_{\bar{∂}}(Ω)$ on a regular convex cone Ω with the Cheng–Yau metric for 𝑝 > 𝑞.

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© 2019 The Mathematical Society of Japan
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