报告名称：Combinatorial Calabi flow with surgery on surfaces

主办单位：数学与统计学学院

报告专家：徐旭

专家所在单位：武汉大学 数学与统计学院

报告时间：2020年10月15日(周四)上午10：00-12：00

报告地点：腾讯会议 会议号：523 294 554

专家简介：徐旭，现任武汉大学数学与统计学院副教授，其主要研究兴趣为离散几何与微分几何。解决了关于三维流形上相切型堆球度量整体刚性的Cooper-Rivin猜想；给出了曲面上反演距离大于-1时关于反演距离堆圆度量刚性的Bowers-Stephenson猜想的两个不同证明；通过手术解决了闭曲面上顶点伸缩情形的组合Calabi流对任意初值的收敛性并证明了沿组合Calabi流所需手术次数的有限性。部分工作接收发表在J. Differential Geom.、Adv. Math.、J. Funct. Anal.、Int. Math. Res. Not. IMRN、Calc. Var. Partial Differential Equations、Math. Res. Lett.等刊物上。

报告摘要：Computing uniformization maps for surfaces has been a challenging problem and has many practical applications. In this talk, we will use combinatorial Calabi flow for vertex scaling to approach this problem. To handle the possible singularies along the combinatorial Calabi flow, we do surgery on the flow by edge flipping. We will prove that for any initial flat or hyperbolic cone metric on a closed surface, the combinatorial Calabi flow with surgery exists for all time and converges exponentially fast after finite number of surgeries. The convergence is independent of the initial triangulation on the surface. The talk is based on a joint work with Xiang Zhu.

邀请人：陈立