Study on the theory of conformal embeddings of a Riemann surface focused on the hyperrbolic metric and hydrodynamics of viscous fluids

黎曼曲面共形嵌入理论研究，重点关注粘性流体的双曲度量和流体动力学

基本信息

批准号：
16540157
负责人：
SHIBA Masakazu
金额：
$ 2.37万
依托单位：
Hiroshima University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

Our main purpose was to study conformal embeddings of a Riemann surface into another and hydrodynamics of viscous fluids. Concerning the first topic, we obtained the notion of "circularizable domains" on a Riemann surface and showed that these domains play an important role in the proof of classical Riemann mapping theorem and give a new tool in the construction of fundamental domains for a discontinuous group of conformal automorphisms … such as Fuchsian groups. The second topic is based on the insight that the various area theorems in the theory of conformal embedding will be closely connected with the viscous fluid flows in a tube. The conjecture was first verified in the fall of 2006. We have succeeded in determining the viscosity of the fluid in a tube which realizes the absolute area theorem due to the head investigator. We have thus obtained generalization of the Poiseuille flows. The results have been announced in an international meeting held in Germany and also in the Fall Meeting, Mathematical Society of Japan. Besides, as an application of the theory of conformal embedding, we determined a necessary and sufficient condition for a complex linear combination of extremal parallel slit mappings, which gives a solution to a problem of Maitani.

我们的主要目的是研究riemann表面花药和粘性流体的流体动力学的共形嵌入。不连续的组合自动组的基本领域……fuchsian群体是基于洞察力的洞察力在2006年秋天进行了验证。在秋季，在秋季会议上举行的一个副词中，我们已经宣布了对结果的绝对区域日本。作为保形嵌入理论的应用，我们确定了极端平行缝隙映射的复杂线性组合的必要条件，这为Maitani问题提供了解决方案。

项目成果

期刊论文数量（76）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Maitani : Variation of Bergman metrics on Riexnann surfaces

Maitani：Riexnann 表面上 Bergman 度量的变化

DOI：
发表时间：
2004
期刊：
fath. Ami. 330
影响因子：
0
作者：
T.Ide;H.Isozaki;S.Nakata;S.Siltanen;G.Uhlmann;H. Yamaruchi F. Maitani
通讯作者：
H. Yamaruchi F. Maitani

A Sequence of Behavior Spaces and the Structure of Its Convergent Soace

行为空间序列及其收敛空间结构

DOI：
发表时间：
2006
期刊：
Mem. Fac. Eng. and Design Kyoto Inst. Tech. 54
影响因子：
0
作者：
Matsui;K.
通讯作者：
K.

Conformal slit mapping from periodic domains

周期域的共形狭缝映射

DOI：
发表时间：
2005
期刊：
Kodai Mathematical Journal 28・2
影响因子：
0
作者：
Kazunori ANDO;Akira IWATSUKA;Masahiro KAMINAGA;Fumihiko NAKANO;Fumio MAITANI
通讯作者：
Fumio MAITANI

Hyperbolically maximal domains on Riemann surfaces

黎曼曲面上的双曲最大域