Narrow Results

In this paper, we establish two new versions of Landau-type theorems for pluriharmonic mappings with a bounded distortion. Then using these results, we derive three Bloch-type theorems of pluriharmonic mappings, which improve the corresponding results of Chen and Gauthier.

The author obtains the theorems of Barth-Lefschetz type on Kähler manifolds with partially positive bisectional curvature without the assumption of nonnegative bisectional curvature. Some applications of the results to holomorphic mappings are given.

In this paper, the solutions of the Riemann boundary value problems on infinite dimensional locally convex spaces into other infinite dimensional locally convex spaces are presented, via piecewise holomorphic mappings on infinite dimensional locally convex spaces, except for infinite dimensional locally convex manifolds as a boundary, where a key concept-the infinite dimensional index of a mapping is defined.