Spectral inequality for Dirac right triangles

What is it about?

We consider a Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimized by the isosceles right triangle under the area or perimeter constraints. We prove this conjecture under extra geometric hypotheses relying on a recent approach of Briet and Krejcirik [J. Math. Phys. 63, 013502 (2022)]. Additionally, we have proven that the square of the operator on polygons has the same form as it does on smooth domains.

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