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

Abstract: We show vanishing theorems of $L^2$-cohomology groups of Kodaira-Nakano type on complete Hessian manifolds. We obtain further vanishing theorems of $L^2$-cohomology groups $L^2H^{p,q}(\Omega)$ on a regular convex cone $\Omega$ with the Cheng-Yau metric for $p>q$.