We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds. Previously in [Br3] similar results were established for some domains on coverings of St...

Let X be a connected normal complex space of dimension n ≥ 2 which is (n − 1)-complete, and let π : M → X be a resolution of singularities. By use of Takegoshi’s generalization of the Grauert-Riemenschneider vanishing theorem, we deduce H cpt(M,O) = 0, which in turn implies Hartogs’ extension theorem on X by the ∂-technique of Ehrenpreis.

This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show existence of a Kähler–Einstein metric On other hand, calculate explicit expression for Rawnsley’s ε-function, and then give sufficient necessary condition to be balanced. an application, also find that there exist triangles being both

In this paper we prove a metric version of Hartogs’ theorem where the holomorphic function is replaced by locally symmetric Hermitian metric. As an application, that if Kobayashi on strongly pseudoconvex domain with $${\mathcal {C}}^2$$ smooth boundary Kähler metric, then universal cover unit ball.