2020-2021第二学期几何讨论班
时间：2021. 3.17
地点：理工南楼616
主讲人：王鹏
题目：Willmore stability of minimal surfaces in spheres.
摘要：In this talk, we will discuss the Willmore stability of minimal surfaces in spheres. We will show that the Clifford torus is the unique minimal torus which is not full and locally Willmore minimizer in a sphere.
时间：2021. 3.31
地点：理工南楼616
主讲人：王鹏
题目：On Willmore problem for symmetric surfaces in S^3
摘要：The generalized Willmore conjecture states that the Lawson minimal surfaces $\xi_{g,1}$ minimizes the Willmore energy for all immersions in $S^3$ with genus $g\in\Z^+$. We show that it holds for $f:M\rightarrow S^3$ if $M$ is of genus $g>1$ and $f$ is symmetric under the symmetric group $ {G}_{g,1}$ action. Here $ {G}_{g,1}$ denote the symmetric group of $\xi_{g,1}$ generated by reflections of circles of $S^3$, used in Lawson's original construction of $\xi_{g,1}$. This is a joint work with Prof. Kusner.
时间：2021.4.14
地点：理工南楼616
主讲人：钟景洋
题目：A sphere theorem for Bach-flat manifolds with positive constant scalar curvature.
摘要：In this talk, we will show that a closed Bach-flat Riemannian manifold with constant scalar curvature, when the norm of E and W satisfy some condition, this manifold is isometric to a quotient of the round sphere.
时间：2021.4.21
地点：理工南楼616
主讲人：吴国强
题目：Some results on gradient Ricci Soliton
摘要：In this talk, we will consider Ricci soliton. The first result is the classification of kahler
shrinking gradient Ricci soliton with nonnegative bisectional curvature, which is joint with Prof Shijin Zhang.Then I focus on the splitting results for soliton. If the integral of Ricci curvature along the geodesic line is nonnegative, then the splitting resulthold for Ricci soliton. Under some weak pinching condition on the Ricci curvature, we obtain that the soliton has only one end.
