Mathematical Sciences: Complex Hyperbolicity and Manifolds of Negative Curvature

[505067 Yeung]提出的研究方向是复杂微分几何。研究者试图证明一个足够高次的泛型超平面在射影空间中的补是双曲的。这是经典皮卡德定理在函数论中的自然推广；最近由杨和萧在二维中证明了。复杂双曲流形理论中的许多问题可以看作是值分布问题，因此它们也与丢番图近似理论有关。丢番图近似是数论中处理整数方程的一个重要分支；数学家们最近发现了丢番图方程和复杂解析几何之间深刻而意想不到的关系。

9505067 Yeung The proposed research lies in complex differential geometry. The investigator seeks to prove that the complement of a generic hyperplane of sufficiently high degree in projective space is hyperbolic. This is a natural extension of the classical Picard theorem in function theory; was proved in dimension two recently by Yeung and Siu. Many problems in the theory of complex hyperbolic manifolds can be viewed as value distribution problems, and as such they relate also to diophantine approximation theory. Diophantine approximations are an important subarea of number theory dealing with integer equations; mathematicians have recently uncovered a deep and unexpected relation between diophantine equations and complex analytic geometry.