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math.SP2025
Is the optimal magnetic rectangle a square?
David Krejcirik
We are concerned with the dependence of the lowest eigenvalue of the magnetic Dirichlet Laplacian on the geometry of rectangles, subject to homogeneous fields. We conjecture that t…
math.SP2024
Quasi-conical domains with embedded eigenvalues
David Krejcirik, Vladimir Lotoreichik
The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that…