报告题目:Area-minimizing Cones Associated with Grassmannians
主 讲 人:焦晓祥
单 位:中国科学院大学数学科学学院
时 间:12月14日10:00
腾 讯 ID:780-807-526
密 码:2021
摘 要:
This talk is based on the recent works with Hongbin Cui, Jialin Xin. We introduce our recent works on the minimizing cones associated with Grassmannians based on Gary R. Lawlor’s Curvature Criterion. From an ancient point view of Hermitian orthogonal projectors, we studied standard spherical, minimal embedded Grassmannians of subspaces G(n,m; F)(F=R,C,H), Cayley plane OP^2, and reproved the area-minimization of their cones. Also, based on the work of Wei-Huan Chen, we supply the research on minimizing cones over general oriented real Grassmannians, which is a brand-new result. Moreover, the cones over minimal product of these standard embedding maps are also studied, and we proved that those cones, of dimension no less than eight, are minimizing. Some minimizing cones of dimension seven are also gained, these results are sharp nowadays.
简 介:
焦晓祥,中国科学院大学数学科学学院教授,博导。主要研究方向是子流形几何,研究复Grassmann流形包括四元素射影空间和超二次曲面中的极小二维球面的几何性质和常曲率极小二维球面的分类。在国际重要期刊Math Ann,TAMS,Math Z,JGEA等杂志上发表了学术论文。首次提出复Grassmann流形包括四元素射影空间和超二次曲面中的全无分枝点的共形极小二维球面的几何概念,并与李明艳副教授、崔洪斌博士等人合作首次发现在四元素射影空间HP^3和超二次曲面Q_4中存在非齐次的全无分枝点的常曲率极小二维球面以及在Q_4中极小而在CP^5中不极小的常曲率二维球面。最近,在校准几何方面做了一些研究,发现了定向实Grassmann流形张成的锥不稳定的极小锥以及维数大于等于7的(实、复、四元素)Grassmann流形乘积张成的锥都是面积极小的。主持或参与多项国家自然科学基金面上项目和重点项目的研究。