Geometry and Analysis seminar: Rigidity theorems of spacelike self-shrinkers in pseudo-Euclidean space

Speaker: Hongbing Qiu (Wuhan University)

Time: 2025-10-31 11:10-12:10
Location: 1310, SIMIS

Abstract: For a spacelike m-submanifold M in pseudo-Euclidean space, there are several global conditions : closed one with Euclidean topology; entire graph; complete with induced Riemannian metric. In this talk, we focus on spacelike self-shrinkers for the latter two conditions. Firstly, we show that any complete spacelike self-shrinker M is an affine m-plane by using a new Omori–Yau type maximum principle. Secondly, for general spacelike entire self-shrinking graphs, we establish a new volume growth estimate, then by using this estimate and the Co-Area formula, we prove various rigidity results for spacelike entire self-shrinking graphs. This talk is based on joint works with Prof. Q. Chen and Prof. L. Sun.

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邱红兵，武汉大学副教授，博士生导师，研究方向是微分几何，特别是在子流形几何、平均曲率流和广义调和映照等相关领域。曾先后长期访问德国莱比锡马普数学研究所和美国麻省理工学院数学系。已在 Adv. Math., J. Funct. Anal., Calc. Var. PDE, Math. Res. Lett., J. Geom. Anal. 等国际期刊上发表 SCI 论文二十余篇。主持国家级 (含面上项目 2 项) 和省部级 项目各 4 项。