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math.DG2018★ 10 cited
Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
Svetlana Jitomirskaya, Wencai Liu
We prove sharp criteria on the behavior of radial curvature for the existence of asymptotically flat or hyperbolic Riemannian manifolds with prescribed sets of eigenvalues embedded…
math.DG2017★ 2 cited
Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of the initial energy
Wencai Liu
In this paper, energy function is used to investigate the eigen-solutions of on the Riemannian manifolds. We give a new way to prove the positivity of the initial ener…
math.DG2017★ 2 cited
Growth of the eigensolutions of Laplacians on Riemannian manifolds I: construction of energy function
Wencai Liu
In this paper, we consider the eigen-solutions of , where is the Laplacian on a non-compact complete Riemannian manifold. We develop Kato's methods on manifold and…