Mathematical Sciences: Line Bundle Convexity of Kahler Manifolds

本文主要研究l -凸流形的函数理论性质。这些l -凸流形是相对于束l的各部分是凸的复流形。l -凸流形最近被证明在解决一些同态凸性的经典问题上是有用的，例如Levi问题和Shafarevich关于射影变簇的泛覆盖空间的猜想。该项目涉及五个研究领域：耗尽函数、剖面逼近、嵌入、与连贯分析层值的上同调以及局部边界条件的表征。本研究是在曲面或流形的几何分析的一般领域。这些流形或曲面存在于二维、三维或多维空间，并涉及解析和几何技术来理解和描述它们的结构。通常给定曲面的坐标和度量，以提供距离或角度的度量。在这个项目中，流形在复场上有坐标，并支持厄米度规。

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.