Abstract
AbstractWe revisit the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings and give an explicit new construction of the unstable mode of the inner catenoid by studying the spectrum of an exactly solvable one-dimensional Schrödinger operator with an asymmetric Darboux–Pöschl–Teller potential.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Mathematical Physics
Reference10 articles.
1. Bérard, P., Sa Earp, R.: Lindelöf’s theorem for hyperbolic catenoids. Proc. Am. Math. Soc. 138, 3657 (2010). https://doi.org/10.1090/S0002-9939-2010-10492-6
2. Darboux, G.: Sur une proposition relative aux équations linéaires. Comptes rendus de l’Académie des Sciences - Series I - Mathematics 94, 1456 (1882)
3. Gaillard, P., Matveev, V.B.: Wronskian and Casorati determinant representations for Darboux-Pöschl-Teller potentials and their difference extensions. J. Phys. A: Math. Theor. 42, 404009 (2009). https://doi.org/10.1088/1751-8113/42/40/404009
4. Goldschmidt, B.: Determinatio superficiei minimae rotatione curva data duo puncta jungentis circa datum axem artae. Dissertation, Göttingen (1831)
5. Hoppe, J.: Lectures on minimal surfaces. arXiv:1903.12062 [math.DG] (2019). https://doi.org/10.48550/arXiv.1903.12062