3 problems

Let $\Omega\subset\mathbb{R}^3$ be the cylindrical domain … where $\Omega_p\subset\mathbb{R}^2$ is a Lipschitz polygon. Suppose that each partition-of-unity function $\chi_\ell$ de…

Local embeddability conjecture. A CR 3-space admits locally a closed, non-zero section of its canonical bundle if and only if it is locally embeddable.

Fix $M>0$. Let $\eta\in(0,1)$ and $m\in\mathbb{Z}$. Let $J_2,J_3\geq J_1\geq J_{\mathrm{min}}\geq 1$, and let $C=C(m,M,J_1,J_2,J_3,\eta)>0$. For any $|a|\leq M$ and any solution…