Constant Mean Curvature Surfaces and Smoke Ring Flow

柏林理工大学数学系的微分几何研究小组将微分几何的思想应用到计算机图形学中，并利用可视化技术进行微分几何实验，取得了很大的成功。这导致了数学中一个新的研究领域的发展，称为离散微分几何。二十多年来，微分几何课题组与中国的同事们进行了非常成功的合作。这个项目的目的是将这种合作扩展到离散微分几何和计算机图形学的相互作用。拟议的项目由三个密切相关的部分组成。第一部分是关于我们与中国领先的微分几何学家的合作扩展到离散微分几何和可视化的新领域。第二部分是关于常平均曲率曲面理论与空间曲线烟环流动关系的研究。这个具体的研究项目依赖于微分几何和可视化的相互作用，因此它实现了上面概述的想法，并为该项目内的其他活动提供了一个研究锚。在第三部分中，我们希望继续我们与中国领先的微分几何学家在几何建模程序、子流形和Weyl几何方面的现有合作。

The Differential Geometry research group at the Department of Mathematics at TU Berlin has been very successful in applying ideas from Differential Geometry to Computer Graphics and using visualization to carry out experiments in Differential Geometry. This led to the development of a new research field in mathematics called Discrete Differential Geometry. Since more than two decades the Differential Geometry research group is having a very successful cooperation with colleagues in particular from China. The aim of this project is to extend this cooperation to the interplay of Discrete Differential Geometry and Computer Graphics. The proposed project consists of three strongly related parts. The first part concerns the extension of our cooperation with leading Differential Geometers in China into the new field of Discrete Differential Geometry and Visualization. The second and central part is a research project on the relation of the theory of surfaces of constant mean curvature and the smoke ring flow of space curves. This concrete research project relies on the interplay of Differential Geometry and Visualization, thus it implements the ideas sketched above and provides a research anchor for other activities within this project. In the third part we want to continue our existing cooperation with leading Differential Geometers in China concerning Geometric Modelling Procedures, Submanifolds and Weyl Geometries.