Speaker: Hongbing Qiu（Wuhan University）
Time: 14:00-15:00, Nov 17, 2022
Room: Tencent Meeting: 306-162-953, no password
In this talk, we shall discuss rigidity results of translating solitons of the mean curvature flow. Translating solitons can be regarded as minimal submanifolds if we make a conformal change of the metric of the ambient space. This important observation is due to Ilmanen. One special class of translating solitons with higher codimension is the symplectic translating solitons, which are solutions to symplectic MCFs, we obtain a rigidity result of symplectic translating solitons via the complex phase map, which indicates that if the cosine of the Kähler angle has a positive lower bound, then any complete symplectic translating soliton with nonpositive normal curvature has to be an affine plane. In general, we study the translating solitons via the Gauss map, and we prove a Bernstein type theorem for complete translating solitons, whose images of their Gauss maps are contained in an appropriate neighborhood of the Grassmannian manifold.
