基础数学系学术报告

及微分几何讨论班（第15讲）

题目： Finite-time singularity of 2-d harmonic map flow into Kahler manifolds

报告人：宋翀 （厦门大学）

报告时间：2020年12月31日14:00-15:00

报告地点：（腾讯会议ID：999 816 846）

摘要：It is well-known that 2d harmonic map flow may develop singularities in finite time. In 1990s, Ding-Tian and Lin-Wang proved the energy identity at finite time singularities. However, Topping showed that the blow-up behavior can still be quite wild in general. Suppose the target manifold is a compact Kahler manifold with non-negative holomorphic bisectional curvature. We show that if a 2-d harmonic map flow with low initial d-bar energy blows-up at a finite time, then it converges to a Holder continuous map in the sense of bubble-tree with no neck. This is a joint work with Alex Waldron.

报告人简介：宋翀，厦门大学副教授，2009年在中科院获得博士学位，导师是田刚院士和王友德研究员。研究方向为几何分析，特别是具有几何物理背景的偏微分方程的爆破分析问题，在Yang-Mills-Higgs场论、薛定谔型几何流等研究领域取得了原创性成果；在Math. Ann., Ann. Inst. H. Poincare-NA, J. Funct. Anal., Calc. Var. PDEs, Int. Math. Res. Not.等学术期刊上发表论文十余篇。

邀请人：沈良明