Spectral inequality for Dirac right triangles

Tuyen Vu

doi:10.1063/5.0147732

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arXiv · 2302.13040

Spectral inequality for Dirac right triangles

Tuyen Vu

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Abstract

We consider the Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimised by the isosceles right triangle both under the area or perimeter constraints. We prove this conjecture under extra geometric hypotheses relying on a recent approach of Ph. Briet and D. Krej{\v{c}}i{\v{r}}{\'i}k for Dirac rectangles [2].

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Tuyen Vu. 2023-02-25. Spectral inequality for Dirac right triangles. https://doi.org/10.1063/5.0147732

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