Curved nonlinear waveguides Baldelli, Laura Krejčiřík, David D.K. was supported by the EXPRO grant No. 20-17749X of the Czech Science Foundation. This work has been partially carried out during a stay of L.B. in Prague at the Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague. She would like to express her deep gratitude to this prestigious institution for its support and warm hospitality. L.B. is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). L.B. was partially supported by National Science Centre, Poland (Grant No. 2020/37/B/ST1/02742), by INdAM-GNAMPA Project 2023 titled Problemi ellittici e parabolici con termini di reazione singolari e convettivi (E53C22001930001) and by the IMAG-Maria de Maeztu Excellence Grant CEX2020-001105-M funded by MICINN/AEI . The Dirichlet -Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the essential spectrum is positive whenever the cross-section is centrally symmetric and the tube is asymptotically straight, untwisted and non-trivially bent. Second, a Hardy-type inequality is derived for unbent and non-trivially twisted tubes. 2025-04-25T09:28:51Z 2025-04-25T09:28:51Z 2025-09 journal article L. Baldelli and D. Krejčiřík. Nonlinear Analysis 258 (2025) 113814. https://doi.org/10.1016/j.na.2025.113814 https://hdl.handle.net/10481/103798 10.1016/j.na.2025.113814 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier