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Talks by Kazuo Akutagawa

Geometric relative Hardy inequalities and the discrete spectrum of Schrödinger operators on manifolds

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 Δ=div\Delta = \mathrm{div}\nabla on Rn\mathbb{R}^n shows the borderline-behavior of a potential VV for the following question : whether the Schrödinger operator Δ+V-\Delta + V has a finite or infinite number of the discrete spectrum. In this talk, we will show a sharp generalization of this inequality on Rn\mathbb{R}^n to a relative version of that on large classes of complete noncompact manifolds. Replacing Rn\mathbb{R}^n by some specific classes of complete noncompact manifolds, including hyperbolic spaces, we also show some sharp criteria for the above-type question.

Kazuo Akutagawa

Tokyo Institute of Technology (Japón)

Number of talks
1

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This activity is supported by the research projects EUR2024.153556, PID2023-150727NB-I00, , PID2023-151060NB-I00, PID2022-142559NB-I00, CNS2022-135390 CONSOLIDACION2022, PID2020-118137GB-I00, PID2020-117868GB-I00, PID2020-116126GB-I00.