幾何学コロキウム：Cauchy problems for surfaces related to harmonic maps（David Brander 氏，Technical University of Denmark）

開催日時

2018年10月15日 17時00分 ～ 18時00分

場所

理学部３号館３－２０４室

講演者

David Brander (Technical University of Denmark)

Abstract:
Harmonic maps from Riemannian or Lorentzian surfaces into Symmetric spaces admit loop group generalizations of the classical Weierstrass representation Riemannian) or d’Alembert solution of the wave equation (Lorentzian).

These allow one to construct solutions to the various geometric problems that are associated to harmonic maps. The utility of these representations is obstructed by the loss of geometric information in the loop group decomposition

that relates the harmonic map to the “Weierstrass” data. However, it is possible to introduce special types of Weierstrass data that contain full geometric information along a curve. I will discuss applications of this technique to the construction of integrable surfaces, such as Willmore surfaces and surfaces of constant curvature, as well as surfaces with prescribed singularities.