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Journals and Conferences
Consider a one dimensional quantum mechanical particle described by the Schrödinger equation on a closed curve of length 2π. Assume that the potential is given by the square of the curve’s curvature.… (More)
The purpose of this manuscript is to present a series of lecture notes on isoperimetric inequalities for the Laplacian, for the Schrödinger operator, and related problems.
Let Ω be some domain in the hyperbolic space Hn (with n ≥ 2) and S1 the geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the Payne-Pólya-Weinberger conjecture for Hn, i.e.,… (More)