Second main theorem and uniqueness problem of meromorphic mappings with moving hypersurfaces

In this article, we establish some new second main theorems for meromorphic mappings of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n(\mathbb{C})$ and moving hypersurfaces with truncated counting functions. A uniqueness theorem for these mappings sharing few moving hypersurfaces without counting multiplicity is also given. This result is an improvement of the recent result of Dethloff - Tan [3]. Moreover the meromorphic mappings in our result may be algebraically degenerate. The last purpose of this article is to study uniqueness problem in the case where the meromorphic mappings agree on small identical sets.