中科院数学与系统科学研究院
数学研究所
几何分析研讨班
报告人：宋 翀 副教授 (厦门大学)
题 目：Finite-time singularity of 2-d harmonic map flow into Kahler manifolds
时 间：2020.11.26（星期四）, 14:00-15:00
地 点：腾讯会议ID：902 733 724
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.
报告人简介：宋翀副教授的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。
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报告人： 罗 勇 副教授 (重庆理工大学数学科学研究中心)
题 目：On minimal Lagrangian surfaces in with capillary boundary on
时 间：2020.11.26（星期四）, 15:00-16:00
地 点：腾讯会议ID：902 733 724
摘 要：We talk about minimal Lagrangian surfaces in with Legendrian capillary boundary on S3. On the one hand, we prove that any minimal Lagrangian surface in B4 with Legendrian free boundary on S3 must be an equatorial plane disk. One the other hand, we show that any annulus type minimal Lagrangian surface in B4 with Legendrian capillary boundary on S3 must be congruent to one of the Lagrangian catenoids. These results confirm the conjectures proposed by Li, Wang and Weng (Sci. China Math., 2020). This is a joint work with Sun Linlin.
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