本次計畫我們研究有關擬赫爾米特幾何和柯西黎曼幾何相關的解析問題。在這一方面，我們最近幾年已有了一些突破(見研究計畫內容(一))。我們預計從各個角度出發，但著重在擬赫爾米特結構的緊緻性定理、體積的比較性定理、曲面的自然結構的建立，還有擬調和映射的研究等。第一年我們會依需要建立一些相關的分析工具，然後逐年把重點擺在與觸拓樸相關聯的問題上。我們想要找到ㄧ些觸拓樸的幾何描述。 ; In this research plan, we』ll study the analytic problems related to Pseudohermitian geometry and CR geometry. We have made progress in this field for these past years. We』ll study a variety of problems, but pay our attention exclusively on the compactness theorem for pseudohermitian structures、volume comparison theorem、establishing the natural structures on surfaces as well as the study of pseudoharmonic maps…and so on. For the first year, we』ll establish some related analytic tools, then relating our results to contact topology. Ultimately, we wonder if there are some geometric descriptions about contact topology. ; 研究期間 9808 ~ 9907
