Year: 2025
Type: preprint
Abstract: Let $-Δ_{\cal S}$ be the Laplace operator in ${\cal S} \subset \mathbb{R}^3$ 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.
Source: arXiv (Cornell University)
Author: Bello, Diana C. S.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979303913
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