Abstract
We show vanishing theorems of $L^2$-cohomology groups of Kodaira–Nakano type on complete Hessian manifolds by introducing a new operator $\partial'_F$. We obtain further vanishing theorems of $L^2$-cohomology groups $L^2H^{p,q}_{\bar{\partial}}(\Omega)$ on a regular convex cone $\Omega$ with the Cheng–Yau metric for $p>q$.
Citation
Shinya AKAGAWA. "Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds." J. Math. Soc. Japan 71 (1) 65 - 89, January, 2019. https://doi.org/10.2969/jmsj/77397739
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