\(L^2\) harmonic forms on some complete Kähler manifolds
The goal of this paper is to obtain vanishing theorems for \(H^{p,q}_{(2)} (M),\) the space of \(L^{2}\) harmonic \((p,q)\) forms, for \( p+q\) not equal to the middle dimension \(n.\) This is accomplished under the assumption that the metric potential \( \lambda\) ``dominate its gradient'', a boundedness condition which is defined in the paper and which is reminiscent of Gromov's notion of Kähler hyperbolicity. An application is made to the Cauchy-Riemann equation \(\overline{\partial } u = \alpha ,\) and examples are given.
space of \(L^{2}\) harmonic \((p,q)\) forms
scientific article; zbMATH DE number 1801554