Hardy inequalities in tubular domains
by David Krejcirik (Department of Theoretical Physics, Nuclear Physics Intitute, Academy of Sciences, Rez, Czech Republic)
We show that twist of an unbounded tube in the Euclidean space gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Laplacian in locally and mildly bent tubes with non-circular cross-section. We also discuss analogous phenomena induced by curvature of an ambient space or by alteration of boundary conditions.