Quantitative Estimates on the Singular Sets of Alexandrov Spaces

浙江大学数学科学学院九十周年院庆系列活动之五十二

 
题目：  Quantitative Estimates on the Singular Sets of Alexandrov Spaces 
报告人：李楠（CUNY） 
时间：7月9日（周一） 10：00-11：00  
地点： 工商楼4楼报告厅 

摘要： We study the quantitative singular sets $mathcal S^k_epsilon$ for collapsed Alexandrov spaces. We prove a new covering theorem and the packing estimates for $mathcal S^k_epsilon$. We also show that $mathcal S^k_epsilon$ are $k$-rectifiable, and for every $1le kle n-2$, we construct examples for which $mathcal S^k_epsilon$ is a Cantor set with positive $mathcal H^k$-measure. This is a joint work with Aaron Naber.