Analysis on Riemann surfaces and manifolds to gether with contributions to physics and engineeing

我们用函数论的方法对曲面和流形上的各种流体动力学现象有了新的认识。具体地说，我们对平面和黎曼曲面上的Rankine卵形很感兴趣。我们使用函数论技术(由首席研究员发起)来从物理和数学上研究这一现象。物理研究是基于汇和源、涡旋、能量、力矩等概念，而数学研究是基于我们目前所获得的结果。其中最重要的是对紧黎曼曲面的研究，其中规定的非紧黎曼曲面可以共形嵌入其中。我们证明了任何Rankine卵球形都可以由单连通平面区域上的单叶亚纯函数来实现，并且Rankine卵球形的面积出奇地接近于某些竞争函数族可能达到的最大面积。这一结果是在塞浦路斯尼科西亚举行的“计算方法和函数理论(CMFT‘97)”国际会议上宣布的，并将被列入会议记录。

We used the function-theoretic methods to obtain a new insight into the various fluid-dynamical phenomena on surfaces and manifolds. Specifically, we have been interested in Rankine ovoids on plane and Riemann surfaces. We use the function-theoretic technique (initiated by the head investigator) to study the phenomenon physically as well as mathematically. The physical investigation is based on the notions of sink and source, vortex, energy, moment and so on, while the mathematical investigation is based on our own results which have been so far obtained. Of the most importance among them is the study of compact Riemann surfaces into which a prescribed noncompact Riemann surface can be conformally embedded. We have proved that any Rankine ovoid can be realized by a univalent meromorphic function on a simply connected plane domain and that the area of the Rankine ovoid is surprisingly close to the possible maximum area which will be attained in a certain family of competing functions. The result was announced at the International Conference "Computational Methods and Function Theory (CMFT'97)" held in Nicosia, Cyprus, and will be included in the Proceedings.