Journal of the Mathematical Society of Japan

Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds

Shinya AKAGAWA

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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 $p>q$.

Article information

Source
J. Math. Soc. Japan, Volume 71, Number 1 (2019), 65-89.

Dates
Received: 22 February 2017
Revised: 4 June 2017
First available in Project Euclid: 26 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1540541021

Digital Object Identifier
doi:10.2969/jmsj/77397739

Mathematical Reviews number (MathSciNet)
MR3909915

Zentralblatt MATH identifier
07056558

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

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

Citation

AKAGAWA, Shinya. Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds. J. Math. Soc. Japan 71 (2019), no. 1, 65--89. doi:10.2969/jmsj/77397739. https://projecteuclid.org/euclid.jmsj/1540541021


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References

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