Class of hypocomplex structures on the two dimensional torus

Abdelhamid Meziani; Giuliano Zugliani

Class of hypocomplex structures on the two dimensional torus

Analysis of PDEs 2019-02-12 v1

Authors: Abdelhamid Meziani , Giuliano Zugliani

Abstract

We study the H\"{o}lder solvability of a class of complex vector fields on the torus $\mathbb{T}^2$ . We make use of the Theta function to associate a Cauchy-Pompeiu type integral operator. A similarity principle for the solutions of the equation $Lu=au+b\bar{u}$ is obtained.

Keywords

theta correspondence algebraic tori vector fields

Cite

@article{arxiv.1902.03922,
  title  = {Class of hypocomplex structures on the two dimensional torus},
  author = {Abdelhamid Meziani and Giuliano Zugliani},
  journal= {arXiv preprint arXiv:1902.03922},
  year   = {2019}
}

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