3 problems

Let $h:\mathbb{R}^n\to\mathbb{R}$ be a real polynomial, and let $d_h=d+dh\wedge\cdot$ act on the de Rham complex of tempered currents on $\mathbb{R}^n$. For sufficiently large…

Conjecture 2. For a generic family of pairs $(g,f)$, the positive eigenvalue branches and therefore their corresponding eigenform branches have multiplicity one.

Conjecture 1. The set $cal A^q(infty)$ is empty.