Mathematical Sciences: Geodesics and Minimal Surfaces in Manifolds with Non-negative Curvature

点击翻译按钮获取中文摘要

The principal investigator intends to continue his study of geodesics and minimal surfaces in manifolds of non-negative curvature with particular emphasis on manifolds of dimension four. Minimal surface theory will be used to investigate the relationships between the sectional curvature and topology of a manifold. A minimal surface is a surface which may be characterized as one which has minimal surface area for any bounding curve on the surface. It may also be characterized as one which minimizes the "surface tension" energy or which has mean curvature zero. In some sense, a minimal surface is a two dimensional analog of a geodesic, a curve of least length joining two points. The principal investigator will use the theory of minimal surfaces to study relationships between the global properties of a space and local properties such as curvature.