Global solvability of real analytic involutive systems on compact manifolds. Part 2

Abstract:

This work continues a previous study by Hounie and Zugliani on the global solvability of a locally integrable structure of tube type and a corank one, considering a linear partial differential operator $\mathbb L$ associated with a real analytic closed $1$-form defined on a real analytic closed $n$-manifold. We deal now with a general complex form and complete the characterization of the global solvability of $\mathbb L.$ In particular, we state a general theorem, encompassing the main result of Hounie and Zugliani.

As in Hounie and Zugliani’s work, we are also able to characterize the global hypoellipticity of $\mathbb L$ and the global solvability of $\mathbb L^{n-1}$—the last nontrivial operator of the complex when $M$ is orientable—which were previously considered by Bergamasco, Cordaro, Malagutti, and Petronilho in two separate papers, under an additional regularity assumption on the set of the characteristic points of $\mathbb L.$