Geometric relative Hardy inequalities and the discrete spectrum of Schrödinger operators on manifolds
Kazuo Akutagawa Tokyo Institute of Technology
This talk is based on a joint work with Hironori Kumura (Shizuoka University, Japan). The classical Hardy inequality for the Laplacian on shows the borderline-behavior of a potential for the following question : whether the Schrödinger operator has a finite or infinite number of the discrete spectrum. In this talk, we will show a sharp generalization of this inequality on to a relative version of that on large classes of complete noncompact manifolds. Replacing by some specific classes of complete noncompact manifolds, including hyperbolic spaces, we also show some sharp criteria for the above-type question.