报告人：Hojoo Lee BK助理教授
首尔国立大学
题目: Complex analysis of minimal surfaces and flat structures（系列报告）
时间：2019年02月18日下午14:30-15:30
2019年02月18日下午16:00-17:00
2019年02月19日下午11:00-12:00
地点：海韵实验楼108
摘要: Minimal surfaces become stationary solutions of the mean curvature flow and mathematical models for Plateau’s soap film experiments, as natural higher dimensional generalization of geodesics. The modern theory of minimal surfaces offers spectacular applications to, for instance, the three dimensional topology and geometry (by Meeks, Scheon, Simon, Yau), positive mass conjecture in mathematical relativity (by Scheon, Yau), and the Ricci flow proof of Poincare’s conjecture (by Perelman). In this mini-course, we present a comprehensive introduction to some of important global results and interesting examples in the minimal surface theory. We sketch several proofs of Bernstein's beautiful theorem that the only entire minimal graphs in Euclidean three-space are flat planes, and present various Bernstein type results in Euclidean four-space, which highlight the role of complex analysis in the modern theory of minimal surfaces. Inspired by the Finn-Osserman (1964), Chern (1969), do Carmo-Peng (1979) proofs of the Bernstein theorem, we prove a new rigidity theorem for associate families connecting the doubly periodic Scherk graphs and the singly periodic Scherk towers. Our characterization of Scherk's surfaces discovers a new idea from the original Finn-Osserman curvature estimate. Combining two generically independent flat structures introduced by Chern and Ricci, we shall construct geometric harmonic functions on minimal surfaces, and establish that periodic minimal surfaces admit fresh uniqueness results.
Recommended Reading List:
[1] Joaquin Perez, A new golden age of minimal surfaces, Notices Amer. Math.Soc. 64 (2017), no. 4, 347-358.
[2] Jeremy Gray, Mario Micallef, About the cover: the work of Jesse Douglas on minimal surfaces, Bull. Amer. Math. Soc. (N.S.) 45 (2008), no. 2, 293-302.
报告人简介：Hojoo Lee是首尔国立大学的BK助理教授。他于2011年在首尔国立大学获得博士学位，先后在西班牙Granada大学，韩国高等研究院（KIAS），英国Warwick大学从事研究工作。他的研究方向是微分几何与几何分析，特别是在极小曲面理论方面取得了非常重要的研究成果。
联系人：夏超教授
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