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

Research Field :
Surface theory


Research Summary :
Using notions of smooth surface theory in differential geometry, I conduct research on discrete and semidiscrete 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 : 

F. Burstall, U. HertrichJeromin and W. Rossman,
Discrete linear Weingarten surfaces, to appear in Nagoya Math J.

S. Fujimori, Y. Kawakami, M. Kokubu, W. Rossman, M. Umehara and
K Yamada, Entire zeromean curvature graphs of mixed type in
LorentzMinkowski 3space, Quart. J. Math. 67 (2016), 801837

F. Burstall, U. HertrichJeromin, C. Muller and W. Rossman,
Semidiscrete isothermic surfaces, Geom. Dedicata 183 (2016), 4358.

F. Burstall, U. HertrichJeromin, W. Rossman and S. Santos,
Discrete special isothermic surfaces, Geom. Dedicata 174
(2015), 111.

S. Fujimori, W. Rossman, M. Umehara, K. Yamada and S.D. Yang,
Embedded triply periodic zero mean curvature surfaces of mixed
type in LorentzMinkowski 3space, Michigan Math. J. 63 (2014),
no. 1, 189207.
 Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3space
(with T. Hoffmann, T. Sasaki and M. Yoshida).
Trans. A.M.S. 364 (2012), 56055644.
 Lie geometry of linear Weingarten surfaces
(with U. HertrichJeromin and F. Burstall).
Comptes Rendus, Acad. Sci. Paris, Ser. I 350 (2012), 413416.
 Lie geometry of flat fronts in hyperbolic space
(with U. HertrichJeromin and F. Burstall).
Comptes Rendus, Acad. Sci. Paris, Ser. I 348 (2010), 661664.
 New maximal surfaces in Minkowski 3space with arbitrary genus and their cousins in de Sitter 3space
(with S. Fujimori, M. Umehara, K. Yamada and SD. Yang).
Result. Math. 56 (2009), 4182.
 Spacelike mean curvature one surfaces in de Sitter 3space (with
S. Fujimori, M. Umehara, K. Yamada and SD. Yang).
Comm. Anal. Geom. 17(3) (2009), 383427.


