3 problems

Polar duality conjecture. The ellipsoids $\Omega_X$ and $\Omega_P$ form a dual pair:

Hardy–polar duality conjecture. Under these assumptions, $(X,P)$ is an $\hbar$-polar quantum pair.

Polar-duality conjecture. If the first sum attains its maximum at a point $N$, then the second sum attains its minimum at $N$, and conversely. If the first sum is independent of th…