Landau-Bloch type theorems for strongly bounded harmonic mappings

摘要

In this paper, we first establish the sharp version of Landau-Bloch type theorem for strongly bounded harmonic mappings by considering the Landau-Bloch type theorem of a one-parameter family of holomorphic mappings. Next, we will establish two sharp versions of Landau-Bloch type theorems for certain harmonic mappings. Finally, we also pose several conjectures for the sharp version of Landau-Bloch type theorem for bounded harmonic mappings.