Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds

2024/11/25 by Cuenin, Jean-Claude
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2411.16984

Abstract

We prove eigenvalue bounds for Schrödinger operator -Δ_g+V on compact manifolds with complex potentials V. The bounds depend only on an L^q-norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank's \citeMR2820160 results in the Euclidean case.

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