Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

DMS-9500491 Shiffman Shiffman将继续他的研究复品种和亚纯映射。 他将调查的kabayashi-royden无穷小pseudometric和小林pseudodistane对获得更好地理解的概念，双曲投影流形的目标。 他还将回到主题的价值分配理论，并将寻求新的缺陷关系的亚纯映射和部分的向量丛。 多复变出现在世纪初作为一个自然的产物研究的职能，一个复杂的变量。 很明显，这个理论与它的前身有很大的不同。 基本的几何是更难以把握和函数理论有更多的亲和力与偏微分算子的一阶。 因此，它成长为一个混合学科结合了微分几何和微分方程的深刻特点。 许多基本结构是在过去三十年中确定的。 目前的研究仍然集中在理解这些基本的数学形式。

DMS-9500491 Shiffman Shiffman will continue his research on complex varieties and meromorphic mappings. He will investigate the Kabayashi-Royden infinitesimal pseudometric and Kobayashi pseudodistane with a goal towards obtaining a better understanding of the concept of hyperbolicity for projective manifolds. He will also return to the topic of value distribution theory and will seek new defect relations for meromorphic maps and for sections of vector bundles. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.