Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem

In this article, we show some new second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ with truncated counting functions. Our results are improvements of recent previous second main theorems for moving hyperplanes with the truncated (to level $n$) counting functions. As their application, we prove a unicity theorem for meromorphic mappings sharing moving hyperplanes.