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On the spectral theory of sign-changing Laplace operators

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arxiv 2502.03838 v1 pith:IMNFHQOW submitted 2025-02-06 math.AP math-phmath.MPmath.SP

Yves Colin de Verdière (IF) This is my paper · ORCID
classification math.APmath-phmath.MPmath.SP
keywords laplaceoperatorssemi-classicalsign-changingspectraltheorydescribedirichlet-to-neumann
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We study spectral theory of sign-changing Laplace operators using semi-classical Dirichlet-to-Neumann maps. We prove the existence of modesconcentrated on the interface and describe an effective semi-classical equation for them.

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  1. Surface plasmons in metamaterial cavities: Scattering by obstacles with negative wave speed

    math.SP 2025-05 accept novelty 8.0 of 10

    In non-trapping metamaterial cavities with negative wave speed, near-real resonances exist exactly when the boundary index exceeds a threshold, are localized at the boundary, and obey a Weyl law.

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