  I explain an open conjecture by Braverman/Milatovic/Shubin (BMS) on the
positivity of square integrable solutions $f$ of $(-\Delta+1)f\geq 0$ on a
geodescially complete Riemannian manifold, and its connection to essential
self-adjointness problems of covariant Schr\"odinger operators. The latter
conjecture has remained open for more than 14 years now.
