Event Details
Title: Integrable system methods for minimal surfaces
Speaker: Katrin Leschke, Leicester University (UK)
Abstract: Harmonic maps into appropriate spaces give rise to integrable systems; in particular, a spectral parameter can be introduced to investigate surfaces given by harmonicity. For example, surfaces with constant mean curvature have harmonic Gauss map. In the case of minimal surfaces the Gauss map does not determine the minimal surface uniquely but for surfaces with for non-vanishing mean curvature integrable system methods can been used to classify all CMC tori as meromorphic functions on the spectral curve. Recently, integrable systems have appeared in minimal surface theory, e.g., in the classification of planar domains or the classification of minimal annuli in $S^2\times R$. To understand and exploit the link between classical tools of minimal surface theory and integrable system methods we propose to study instead of the Gauss map another harmonic map which includes the information of both the Gauss map and the support function of the minimal immersion. This is joint work with K. Moriya, Tsukuba.
25 September 2015, 12:00, Seminario de la primera planta, IEMath-GR
More information about the Geometry Seminar here.
Speaker: Katrin Leschke, Leicester University (UK)
Abstract: Harmonic maps into appropriate spaces give rise to integrable systems; in particular, a spectral parameter can be introduced to investigate surfaces given by harmonicity. For example, surfaces with constant mean curvature have harmonic Gauss map. In the case of minimal surfaces the Gauss map does not determine the minimal surface uniquely but for surfaces with for non-vanishing mean curvature integrable system methods can been used to classify all CMC tori as meromorphic functions on the spectral curve. Recently, integrable systems have appeared in minimal surface theory, e.g., in the classification of planar domains or the classification of minimal annuli in $S^2\times R$. To understand and exploit the link between classical tools of minimal surface theory and integrable system methods we propose to study instead of the Gauss map another harmonic map which includes the information of both the Gauss map and the support function of the minimal immersion. This is joint work with K. Moriya, Tsukuba.
25 September 2015, 12:00, Seminario de la primera planta, IEMath-GR
More information about the Geometry Seminar here.
