Spectrum of the Laplacian in waveguide shaped surfaces

2025/06/23 by Bello, Diana C. S.
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2506.18875

Abstract

Let -Δ_{\cal S} be the Laplace operator in \cal S ⊂ ℝ³ on a waveguide shaped surfaces, i.e., \cal S is built by translating a closed curve in a constant direction along an unbounded spatial curve. Under the condition that the tangent vector of the reference curve admits a finite limit at infinity, we find the essential spectrum of -Δ_{\cal S} and discuss conditions under which discrete eigenvalues emerge. Furthermore, we analyze the Laplacian in the case of a broken sheared waveguide shaped surface.

Citations

• Spectral analysis in broken sheared waveguides
• Geometrically induced discrete spectrum in curved tubes

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