Geometry Colloquium

Seminar information archive ~03/27Next seminarFuture seminars 03/28~

Date, time & place Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.)

2014/11/07

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Shinpei KOBAYASHI (Hokkaido University)
Harmonic maps into the hyperbolic plane and their applications to surface theory (Japanese)
[ Abstract ]
Harmonic maps from two-dimensional Riemannian manifolds into the hyperbolic plane have been well studied. Since constant mean curvature surfaces in the Minkowski space have harmonic Gauss maps into the hyperbolic plane, there exist applications to surface theory.
In 1998, Dorfmeister, Pedit and Wu established the construction method of harmonic maps into symmetric spaces via loop group method. Recently, harmonic maps into the hyperbolic plane appear in various classes of surfaces, e.g., minimal surfaces in the Heisenberg group,
maximal surfaces in the anti-de Sitter space or constant Gaussian curvature surfaces in the hyperbolic space. In this talk I will talk about the general construction method of harmonic maps from surfaces into symmetric spaces via loop group method and the case of the hyperbolic plane in details.