5 problems

D'Angelo's conjecture. One has

Let $\Omega\subset\mathbb{C}^n$ be a bounded pseudoconvex domain with smooth boundary of finite type, and let $f=1$ be the trivial multiplier generated by Kohn's procedures. The or…

Let $\Omega\subset\mathbb{C}^n$ be a bounded pseudoconvex domain with smooth boundary of finite type. A $q$-multiplier is a germ of a smooth function whose product with a $(0,q)$-f…

The enthralled-vector-fields conjecture. The real vector fields $X$ satisfying this estimate coincide on a dense open subset of $M$ with the elements of the…

Let $\mathcal O_n$ be the ring of germs of holomorphic functions at the origin in $\mathbb C^n$, and let $I$ be the ideal generated by $f_1,\dots,f_l\in\mathcal O_n$, where…