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Rigidity of self-shrinking surfaces and its applications - 邱红兵 (武汉大学)

作者:   来源:  时间:2021-07-27

度量几何暑期学术报告

Title: Rigidity of self-shrinking surfaces and its applications
Speaker: 邱红兵 (武汉大学)

Abstract

By the fact that a self-shrinking surface in Euclidean space R^4 is hyper-Lagrangian, we show that the complex phase map of a self-shrinking surface is a generalized harmonic map. Based on this subtle property, we prove a rigidity result of self-shrinking surfaces by restriction of the image under the complex phase map, it not only improves a corresponding rigidity theorem of symplectic self-shrinking surfaces, but also is optimal. As applications, by using the blow up analysis of mean curvature flows and the previous rigidity of self-shrinking surfaces, we show that if the image of the initial closed surface under the complex phase map avoids a closed half great circle, then the corresponding mean curvature flow does not develop any Type I singularity. This restriction of the image under the complex phase map is sharp. Finally, we demonstrate that any hyper-Lagrangian submanifold L^{2n}(n > 1) in a hyperkaehler manifold M^{4n} is complex Lagrangian via a similar idea of the proof of the first Theorem

北京时间:2021年7月27日(周二)上午9:00—11:00
线下报告教室:新教二楼808
线上腾讯会议ID:560 2435 5145    

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