A geometric characterization of discrete Guichard nets and their transformations in integrable geometry

Gudrun从事以下项目：1）离散通道表面的研究，作为与我和Gudrun的前博士的联合工作。维也纳技术大学的顾问Udo Hertrich-Jeromin说。 根据光滑通道表面理论的线索，可以将其看作是当沿着表面的非圆形方向沿着移动时具有不同半径的管，Gudrun建立了为什么一种特定的离散化方式是最佳选择。 Gudrun进一步研究了可能的应用，找到了离散等温通道表面的特征，并找到了与多圆离散网的连接。 这项工作已提交出版。2）离散Guichard三重正交系统的研究，联合工作与约瑟夫赵在科比大学和我自己。 特别是，Gudrun发现了Guichard三重正交系的共形对角曲面可以是极小曲面。3）Guichard网的Combescure变换和Ribaucour变换的研究，是她博士学位的延伸。4）离散R-同余的研究，Gudrun与柏林工业大学的Thilo Roerig合作进行的工作。上述四个项目都是成功的，并引起了Gudrun领域其他研究人员的兴趣。

Gudrun worked on the following projects:1) The study of discrete channel surfaces, as joint work with myself and Gudrun's former Ph.D. advisor Udo Hertrich-Jeromin at the Technical University of Vienna. Following clues from the theory of smooth channel surfaces, which can be thought of as tubes with varying radius as one moves along a non-circular direction of the surface, Gudrun established why one particular way of discretizing is the best choice. Gudrun further examined possible applications, finding a characterization of discrete isothermic channel surfaces, and finding connections with multi-circular discrete nets. This work has been submitted for publication.2) The study of discrete Guichard triply orthogonal systems, joint work with Joseph Cho at Kobe University and myself. In particular, Gudrun made the interesting discovery that the conformal diagonal surfaces of Guichard triply orthogonal systems can be minimal surfaces.3) The study of Combescure and Ribaucour transformations of Guichard nets, as an extension of her Ph.D. thesis.4) The study of discrete R-congruences, work that Gudrun is conducting with Thilo Roerig of the Technical University of Berlin.All four projects described above were successful and are of interest to other researchers in Gudrun's field.