Morse index and heat kernel of constant mean curvature surfaces

点击翻译按钮获取中文摘要

1. The Morse Index of Wente ToriWe find various lower and upper bounds for the index of Wente tori that contain a continuous family of planer principal curves. We then prove a result that gives an algorithm for computing the index sharply.2. Doubly Perodic Minimal SurfacesWe consider the question of existence of embedded doubly periodic minimal surfaces with Scherk-type ends. We extend the existance results of Karcher and Wei to more cases and we find other cases where existance dose not hold.3. Embeddedness of area-minimizing disksWe show that a polygonal Jordan cave C satisfies certain conditions, then the least-area Douglas-Rado disk with boundary C is unique and is a smooth graph. With our result we can apply this method to a wider range of complete catenoid-ended minimal surfaces.