Minimal circumscribed Hermitian ellipsoid of Hartogs domains and an application to an extremal problem

In this paper we construct circumscribed Hermitian ellipsoids of Hartogs domains of least volume and as an application, we obtain the Carathéodory extremal mappings between the Hartogs domains and the unit ball, and also give an explicit formula for calculating the extremal values.

Zeros of Bergman kernels on some Hartogs domains

Explicit Bergman kernels are obtained on some Hartogs domains.For some special cases, zeros of the kernels are considered.

Monotonicity for the Chern-Moser-Weyl curvature tensor and CR embeddings

We give,in this paper,a monotonicity formula for the Chern-Moser-Weyl curvature tensor under the action of holomorphic embeddings between Levi non-degenerate hypersurfaces with the same positive signature.As an application,we provide some concrete examples of algebraic Levi non-degenerate hypersurfaces with positive signature that are not embeddable into a hyperquadric of the same signature in a complex space of higher dimension.