Geometry of surfaces with singular points—applications to maximal surfaces in Lorentz-Minkowski space

The authors have collaborated with Kentaro Saji and Wayne Rossman of Kobe University, Shintaro Akamine of Nihon University, Yu Kawakami of Kanazawa University, Masatoshi Kokubu of Tokyo Denki University, Kosuke Naokawa of Hiroshima Institute of Technology, Shoichi Fujimori of Hiroshima University, and Atsufumi Honda of Yokohama National University to research surfaces and hypersurfaces with singular points. In this article, after a brief overview of the authors’ research on criteria for several types of singular points on surfaces, an exposition of their recent work on maximal surfaces in three-dimensional Lorentz-Minkowski space is given.