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Minimal and maximal surfaces with planar curvature lines
概要：
Minimal surfaces with planar curvature lines in the Euclidean 3-space have been studied since the late 19th century, and have surprising connections to different subjects of differential geometry. On the other hand, the classification of maximal surfaces with planar curvature lines in the Minkowski 3-space has only recently been given. In this talk, we first revisit the Euclidean case, and introduce an analytic method to classify these surfaces. Then we apply the analytic method not only to refine the classification of maximal surfaces with planar curvature lines, but also to show that there exists a deformation consisting exactly of all such surfaces. Furthermore, we investigate the types of singularities that appear on maximal surfaces with planar curvature lines.
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