Hamiltonian instability conjecture for non-minimal Lagrangians in indefinite complex space

Let $\mathcal L$ be an H-minimal, non-minimal, Lagrangian submanifold of complex space $\mathbb C^n$ equipped with the pseudo-Kähler structure determined by the Hermitian form

$$\langle\!\langle\cdot,\cdot\rangle\!\rangle_p=-\sum_{j=1}^{p}dz_jd\overline{z}_j+\sum_{j=p+1}^{n}dz_jd\overline{z}_j,$$

where $p\neq 0,n$. Hamiltonian instability conjecture. Then $\mathcal L$ is H-unstable. The preceding theorem establishes this for the homogeneous product tori, while the general assertion for all non-minimal H-minimal Lagrangian submanifolds is presented as an expectation and remains open in the supplied text.