The \(\overline{\partial }\) -Equation on the Hartogs Triangles in \(\mathbb {C}^2\) and \({\mathbb{C}\mathbb{P}}^2\)

This is a survey paper of the recent progress of the Cauchy-Riemann equation on the Hartogs triangles in \(\mathbb {C}^2\) and \({\mathbb{C}\mathbb{P}}^2\) . In particular, \(L^2\) and \(W^1\) Dolbeault cohomology groups on the Hartogs triangles in \({\mathbb{C}\mathbb{P}}^2\) are investigated.