Wayne ROSSMAN

Wayne ROSSMAN

Department of Mathematics,
Graduate School of Science, Kobe University
Division : Geometry
Professor
Building B, Room 420

Personal Website

Research Field : Constant mean curvature surfaces

Research Summary : Using notions of smooth surface theory in differential geometry, I conduct research on discrete and semi-discrete surface theory. In addition to differential geometric methods, tools from integrable systems and analysis and differential equations are used. Prominent types of surfaces in this research are constant mean curvature surfaces, flat surfaces, linear Weingarten surfaces and Omega surfaces. An approach using conserved quantities of flat connections associated with isothermic surfaces is also employed.

Primary Publications :
  1. Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3-space (with T. Hoffmann, T. Sasaki and M. Yoshida). Trans. A.M.S. 364 (2012), 5605-5644.
  2. Lie geometry of linear Weingarten surfaces (with U. Hertrich-Jeromin and F. Burstall). Comptes Rendus, Acad. Sci. Paris, Ser. I 350 (2012), 413-416.
  3. Lie geometry of flat fronts in hyperbolic space (with U. Hertrich-Jeromin and F. Burstall). Comptes Rendus, Acad. Sci. Paris, Ser. I 348 (2010), 661-664.
  4. New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space (with S. Fujimori, M. Umehara, K. Yamada and S-D. Yang). Result. Math. 56 (2009), 41-82.
  5. Spacelike mean curvature one surfaces in de Sitter 3-space (with S. Fujimori, M. Umehara, K. Yamada and S-D. Yang). Comm. Anal. Geom. 17(3) (2009), 383-427.