Infinite Dimensionality of the Middle $L^2$-cohomology on Non-compact Kähler Hyperbolic Manifolds

Abstract

We prove that the space of L 2 harmonic forms of middle degree is infinite dimensional on any non-compact Kähler hyperbolic manifold. §1. Introduction

$L^{2}$ vanishing theorem on some Kähler manifolds

“…Gromov used this notion to show that on the universal covering space of a Kähler hyperbolic manifold, there are no (nontrivial) L 2 -harmonic forms outside the middle degree. In [4], the author showed that the space of L 2 harmonic forms in the middle degree is infinite dimensional. A key argument in Gromov's [18] proof is the following theorem.…”