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January, 2019 Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds
J. Math. Soc. Japan 71(1): 65-89 (January, 2019). DOI: 10.2969/jmsj/77397739


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 $p>q$.


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Shinya AKAGAWA. "Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds." J. Math. Soc. Japan 71 (1) 65 - 89, January, 2019.


Received: 22 February 2017; Revised: 4 June 2017; Published: January, 2019
First available in Project Euclid: 26 October 2018

zbMATH: 07056558
MathSciNet: MR3909915
Digital Object Identifier: 10.2969/jmsj/77397739

Primary: 53C25 , 53C55

Keywords: $L^2$-cohomology groups , Hesse–Einstein , Hessian manifolds , Laplacians , Monge–Ampère equation , regular convex cones

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 1 • January, 2019
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