高端引智Grigor Barseghyan 院士系列讲座一
Three novel trends in complex analysis complementing Nevanlinna- Ahlfors theories. Applications to complex differential equations.
In this lecture, we presented some results related to arbitrary meromorphic functions in a given domain or in the complex plane, which were obtained comparatively recently.
Meromorphic functions in the complex plane were widely studied in the classical theories: since 1890s "French direction" (Picard, Julia, Borel, Milloux results) and since 1920s Nevanlinna value distribution theory (Similar results are also true for functions in the unit disk which satisfy some additional restriction to the growth).
Much less were studied arbitrary meromorphic functions in a given domain: in the 19thcentury the basic results were established by Cauchy; In the 20thcentury we mentioned just the fundamental theorems in Ahlfors theory of covering surfaces (1935).
Since late 1970s some other results of the same generality were established. They can be attributed mainly to three new topics (trends): Gamma-lines, proximity property and universal version of value distribution.
These topics reveal some novel phenomena; Meantime, they complement also the mentioned classical studies.