Some Natural Problems in Complex Geometry

9702836 Yau这个项目是关于复杂几何的研究。更具体地说，研究者要研究Cauchy-Riemann流形的分类问题、复杂的Platform问题和四面体中积分点的估计问题。四面体中整点个数的估计问题在数论和代数几何中都有应用。特别是，这样的估计可以用来寻找更好的素性测试和因式分解算法。复杂的高原问题是复杂几何中的一个基本问题：它试图描述那些可以作为复杂区域边界出现的流形。

9702836 Yau This project deals with research in complex geometry. More specifically, the investigator is to pursue the classification problem for Cauchy-Riemann manifolds, the complex Plateau problem, and the problem of estimating integral points in tetrahedra. The problem of estimating the number of integer points in tetrahedra has applications in number theory as well as algebraic geometry. In particular, such an estimate can be ussed to find better primality testing and factoring algorithms. The complex Plateau problem is a fundamental problem in complex geometry: it seeks to describe those manifolds that can arise as the boundaries of complex domains.