Spectral theory for tensor products of Hermitian holomorphic line bundles

摘要

Let L be a quasipositive line bundle over a compact complex Hermitian manifold. It has been conjectured that the smallest positive eigenvalue of the Laplacian, acting on the k'th tensor power of L, is uniformly bounded independent of k. Various special cases of the conjecture are proved, but a counterexample is given to the general conjecture. [References: 8]