This site contains the schedule and past records of the online seminar "JA, surfaces and beyond". Seminars are held on Wednesdays or Thursdays, about once every 3 or 4 weeks, with a 30-45 minutes presentation on cutting-edge research in the field of geometry of surfaces and related areas. ("JA" = "Japan/Austria")
June 3, 2026 (Wed); 19:00 JST/12:00 CEST : Shintaro Akamine (Nihon University) 赤嶺 新太郎 (日本大学)
Title: Constant mean curvature surfaces in the three-dimensional light cone
Abstract: Some classes of surfaces in spaces equipped with degenerate metrics often arise in correspondence with minimal surfaces in Euclidean space and maximal surfaces in Lorentz-Minkowski space. In this talk, we present local and global properties of spacelike constant mean curvature surfaces in the three-dimensional light cone. In particular, we explain Bernstein-type theorems for such surfaces. This talk is based on the joint work with Wonjoo Lee (Jeonbuk National University) and Seong-Deog Yang (Korea University).
June 17, 2026 (Wed); 19:00 JST/12:00 CEST : Keita Takahashi (Science Tokyo) 髙橋 慶多 (東京科学大学 D2)
Title: TBA
Abstract: TBA
May 6, 2026 (Wed); 19:00 JST/12:00 CEST : Katrin Leschke (University of Leicester)
Title: Links between the integrable systems of a CMC surface
Abstract: A CMC surface in 3-space is constrained Willmore and isothermic. It is well known that these 3 surface classes are each determined by a family of flat connections. In this talk we discuss links between the corresponding families of flat connections: we show that parallel sections of the associated family of flat connections of one family give algebraically the parallel sections of the other families. In particular, we obtain links between transformations of CMC surfaces, isothermic surfaces and constrained Willmore surfaces which are given by parallel sections, such as the associated family, the simple factor dressing and the Darboux transformation.
March 4, 2026 (Wed); 19:30 JST/11:30 CET : Yoshiki Jikumaru (Toyo University) 軸丸 芳揮 (東洋大学)
Title: On the governing equations for membrane O surfaces
Abstract: It is known that a shell membrane in equilibrium where a constant purely normal load qn acts on the membrane, and where the principal curvature lines coincide with the principal stress lines, forms an integrable system called a membrane O surface.
In this talk, we formulate the governing equations for membrane O surfaces of the 1st and 2nd kind, which are analogues to Guichard surfaces of the 1st and 2nd kind introduced by Calapso.
Furthermore, under this formulation, we show that membrane O surfaces are a subclass of Demoulin's Ω surfaces, and that the Bäcklund transformation for membrane O surfaces preserves membrane O surfaces of the 1st and 2nd kind, respectively.
February 11, 2026 (Wed); 19:30 JST/11:30 CET : Joseph Cho (Handong Global University)
Title: Geometry at infinity - from a Minkowski geometric viewpoint
Abstract: Many interesting surface classes in Minkowski 3-space including maximal surfaces and constant mean curvature surfaces are known to admit non-degenerate singularities. These singularities differ from the isolated singularities appearing on analogous surfaces in Euclidean 3-space. However, the case of constant mean curvature surfaces shows that some surfaces in Minkowski 3-space also appear with disconnected components, admitting blow-up points. In this talk, we propose Laguerre geometry to gain insight into the fundamental difference between Euclidean 3-space and Minkowski 3-space, and to obtain an intuitive understanding of why non-degenerate singularities and blow-up points appear on surfaces in Minkowski 3-space. This talk is based on joint work with Wonjoo Lee, Gudrun Szewieczek, and Seong-Deog Yang.
January 28, 2026 (Wed); 19:30 JST/11:30 CET : Yuta Yamauchi (Yokohama National University) 山内 優太 (横浜国立大学 D2)
Title: Minimal total absolute curvature for equiaffine immersions
Abstract: The total absolute curvature is a geometric invariant associated with a compact immersion and a fundamental quantity in global differential geometry. In Euclidean space, it is well known that attaining the minimal value of the total absolute curvature characterizes convex hypersurfaces. Koike defined the total absolute curvature for equiaffine immersions and established a Chern-Lashof type inequality. In this talk, building on Koike's work, I show that minimal total absolute curvature for equiaffine immersions also characterizes convex hypersurfaces.
Online Participation: Zoom link will be emailed to pre-registered participants.