时间：2026年4月21日，周二 下午4:00-5:00

地点：双清综合楼 302

题目： Orthogonal ring patterns and discrete constant mean curvature surfaces

摘要：

We introduce orthogonal ring patterns consisting of pairs of concentric circles. They generalize orthogonal circle patterns which can be treated as a conformal limit. It is shown that orthogonal ring patterns in Euclidean and hyperbolic planes and in a sphere are governed by integrable equations. We deliver variational principles which are used to prove existence and uniqueness results, and also to compute ring patterns with classical boundary conditions. The later are used to generate discrete constant mean curvature surfaces. See the figure demonstrating a pair of corresponding discrete and smooth cmc surfaces. The relation to minimal surfaces in S3 and AdS3 is discussed. Numerous models will be presented. The talk is based on the recent papers:

A.I. Bobenko, Spherical and hyperbolic orthogonal ring patterns: Integrable systems and variational principles, Trans. AMS (2025)

A.I. Bobenko, T. Hoffmann, N. Smeenk, Discrete constant mean curvature

surfaces and orthogonal ring patterns. Geometry from

combinatorics, arXiv:2410.08915 (2024)