数苑讲座之十二：On H-system: an open question of Brezis-Coron and singularity formation

发布时间：2023-11-20 作者：浏览次数：

Speaker	Juncheng Wei院士	DateTime	2023年11月23日（周四）下午4:30
Place	6号楼6401	Abstract	In this talk I will discuss recent advances on $H-$system (surfaces with constant mean curvature) $ \Delta u= H u_x \wedge u_y $ in a two-dimensional domain. First we show that all the $H-$bubbles are non-degenerate and then we consider a problem of singular perturbation in the H-system with Dirichlet boundary condition on disk. As the boundary datum vanishes, we construct higher-degree multi-bubble solutions concentrating at distinct points. This gives a partial answer to a conjecture due to Brezis-Coron and Chanillo-Malchiodi concerning the limiting configuration in the case of higher degrees. Next we construct finite time blow-up for the heat flow of the H-system, describing the evolution of surfaces with constant mean curvature. The singularity at finite time forms as a scaled least energy H-bubble, denoted as W, exhibiting type II blow-up speed. One key observation is that the linearized operators around W projected onto $W^\perp$ and in the W-direction are in fact decoup...

魏军城，著名华人数学家，现任现为加拿大英属哥伦比亚大学国家讲座教授（Canada Research Chair），加拿大皇家科学院院士，主要研究领域是非线性偏微分方程、凝聚现象和爆破以及生物数学等，于2005年获得香港裘槎基金会（Croucher Foundation）“优秀科研者奖”，曾主持国家杰出青年基金，2010年获得华人数学家大会银奖，2010年获得教育部自然科学一等奖，2020年获加拿大数学会的Jefferey-Williams Prize，2014年应邀在第27届国际数学家大会上做45分钟报告，2014年入选国家级领军人才项目。

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