Uniqueness of solutions, radiation conditions, and complexity of the metric at infinity

摘要

The purpose of this paper is to prove the uniqueness theorem of solutions ofeigenvalue equations on one end of Riemannian manifolds for drift Laplacians,including the standard Laplacian as a special case; we shall impose "a sort ofradiation condition" at infinity on solutions. We shall also provide severalRiemannian manifolds whose Laplacians satisfy the absence of embeddedeigenvalues and besides the absolutely continuity, although growth orders oftheir metrics on ends are very complicated.