Title：Value distribution properties for meromorphic maps into the complex projective space
Abstract：Motivated by some results on Gauss maps of minimal surfaces, we first investigate the value distribution properties for the generalized Gauss map of an immersed harmonic surface in Rn. After building a relation between the generalized Gauss map and the classical Gauss map for the K-quasi-conformal harmonic surfaces, we derive that, for a complete K-quasi-conformal harmonic surface immersed in R3, if its unit normal n omits seven directions in S2 and any three of which are not contained in a plane in R3, then the surface must be flat. In addition, some estimates of the Gaussian curvature for the K-quasi-conformal harmonic surfaces in R3 are given. On the other hand, we also study the value distribution of meromorphic maps from C^m into P^n(C). Concerning some truncated counting functions with different weights, we prove a new second main theorem for meromorphic maps, and the uniqueness problem for the case of degenerate meromorphic mappings sharing moving hyperplanes were considered, which can be seen as some improvement of previous results.
报告人：刘志学 讲师 北京邮电大学
地点：腾讯会议 会议 ID：305 122 179