Global hypoellipticity for perturbations of complex vector fields on the torus
Analysis of PDEs
2026-02-25 v1
Abstract
We apply Kr\"{o}necker's approximation theorem to measure (in a topological sense) a set of constants which turn a vector field into a non-globally hypoelliptic operator. We present situations in which this set is a discrete enumerable (hence, meager) subset of the real line, and we also show that this set may be a dense subset of the complex numbers (hence, nonmeager), which produces a contrast to a known result stating that this set has null Lebesgue measure.
Keywords
Cite
@article{arxiv.2602.21159,
title = {Global hypoellipticity for perturbations of complex vector fields on the torus},
author = {Maria V. Bartmeyer and Paulo L. Dattori da Silva and Rafael B. Gonzalez},
journal= {arXiv preprint arXiv:2602.21159},
year = {2026}
}