  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].
