Constant Mean Curvature Surfaces and Smoke Ring Flow

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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.