Mathematical Sciences: Line Bundle Convexity of Kahler Manifolds

本研究将集中在函数的理论性质， L-凸流形 这些L-凸流形是复流形 其相对于束L的部分是凸的。 L-凸 流形最近被证明在攻击一些经典的 同态凸性问题，如Levi问题和 关于泛覆盖空间的Shafarevich猜想 投射簇 该项目涉及五个研究领域： 穷举函数，截面近似，嵌入， 与相干解析层中的值的上同调，以及 通过局部边界条件表征。 本研究属于一般的几何分析领域 表面或流形的。 这些流形或曲面存在于 两个，三个或多个维度，涉及分析和 几何技术来理解和描述它们的结构。 通常，表面被给定坐标和度量， 距离或角度的测量。 在这个项目中， 在复域上有坐标， 公制

This research will focus on function theoretic properties of L-convex manifolds. These L-convex manifolds are complex manifolds which are convex with respect to sections of a bundle L. L-convex manifolds have recently proven useful in attacking some classical problems in homomorphic convexity, such as the Levi problem and Shafarevich's Conjecture on the universal covering space of a projective variety. The project involves five areas of research: exhaustion functions, approximation of sections, embedding, cohomology with values in a coherent analytic sheaf, and characterization by local boundary conditions. This research is in the general area of the geometric analysis of surfaces or manifolds. These manifolds or surfaces exist in two, three, or many dimensions and involve both analytic and geometric techniques to understand and describe their structure. Often the surface is given coordinates and a metric which provides a measurement of distance or angle. In this project the manifolds have coordinates over the complex field and support a hermitian metric.