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

Gudrun参与了以下项目：1)与我和Gudrun在维也纳技术大学的前博士导师Udo Hertrich-Jeromin共同研究离散航道表面。根据光滑通道表面理论的线索，可以将其视为沿表面的非圆形方向移动时具有不同半径的管，古德龙确定了为什么一种特定的离散方法是最佳选择。古德伦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，并找到了与多个圆形离散网络的联系。这项工作已提交出版2)离散Guichard三正交系统的研究，与神户大学的Joseph Cho和我共同工作。特别是，Gudrun做出了一个有趣的发现，即Guichard三重正交系统的共形对角曲面可以是极小曲面。3)作为她博士论文的扩展，Guichard网的Combescure和Ribaucour变换的研究。4)离散R-同余的研究，这是Gudrun与柏林技术大学的Thilo Roerig共同进行的工作。上面描述的所有四个项目都是成功的，Gudrun领域的其他研究人员都感兴趣。

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.