L-2 vanishing theorem on some Kahler manifolds

摘要

Let E be a Hermitian vector bundle over a complete Kahler manifold (X, omega), dim(DOUBLE-STRUCK CAPITAL C)X = n, with a d(bounded) Kahler form omega, and let d(A) be a Hermitian connection on E. The goal of this article is to study the L-2-Hodge theory on the vector bundle E. We extend the results of Gromov [18] to the Hermitian vector bundle. Finally, as an application, we prove a gap result for the Yang-Mills connection on the bundle E over X.