An isoperimetric type inequality for the principal eigenvalue of Schrödinger operators depending on the curvature of a loop

DOI10.1016/j.jde.2015.08.046zbMath1327.81203OpenAlexW1473125594MaRDI QIDQ888192

Vangelis Stefanopoulos

Publication date: 4 November 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.08.046

zbMATH Keywords

Schrödinger operatorisoperimetric inequalityprincipal eigenvalueRiccati equationcurvature of a loop

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Curves in Euclidean and related spaces (53A04) Classical or axiomatic geometry and physics (51P05)

Cites Work

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• On an isoperimetric inequality for a Schrödinger operator depending on the curvature of a loop
• On the Laplace operator penalized by mean curvature
• Dependence of the \(n\)th Sturm-Liouville eigenvalue on the problem
• The second periodic eigenvalue and the Alikakos-Fusco conjecture
• Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator
• A lower bound for the ground state energy of a Schrödinger operator on a loop
• A geometric estimate for a periodic Schrödinger operator
• On the Cauchy Problem for a Dynamical Euler's Elastica
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS

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