English

Extendability and the $\overline \partial$ Operator on the Hartogs Triangle

Complex Variables 2022-01-31 v2

Abstract

In this paper it is shown that the Hartogs triangle T\mathbf T in C2\mathbf C^2 is a uniform domain. This implies that the Hartogs triangle is a Sobolev extension domain. Furthermore, the weak and strong maximal extensions of the Cauchy-Riemann operator agree on the Hartogs triangle. These results have numerous applications. Among other things, they are used to study the Dolbeault cohomology groups with Sobolev coefficients on the complement of T\mathbf T.

Keywords

Cite

@article{arxiv.2106.09867,
  title  = {Extendability and the $\overline \partial$ Operator on the Hartogs Triangle},
  author = {Almut Burchard and Joshua Flynn and Guozhen Lu and Mei-Chi Shaw},
  journal= {arXiv preprint arXiv:2106.09867},
  year   = {2022}
}

Comments

Accepted for publication in Math. Zeit.; 23 pages, typos corrected

R2 v1 2026-06-24T03:20:32.548Z