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Transformation theorems for almost splitting maps and some applications

Abstract

The almost splitting map is a powerful tool in studying manifolds with Ricci curvature uniformly bounded from below and their Gromov-Hausdorff limits. In this talk, we will introduce a new transformation theorem for almost splitting maps, which drops the non-collapsed assumption in the one obtained by Cheeger, Jiang and Naber.  We will also introduce some applications of the new transformation theorem, one of which is a new smooth fibration theorem. More precisely, we introduce a notion, called the generalized Reifenberg condition, under which we prove a smooth fibration theorem for collapsed manifolds with Ricci curvature lower bound. This gives a unified proof of smooth fibration theorems in many previous works, including the classical ones by Fukaya and Yamaguchi respectively. The new transformation theorem is a key tool in its proof. Some other applications of the transformation theorem will be introduced in this talk. This talk is based on my joint work with Hongzhi Huang.

 

报告人简介

黄显涛,中山大学数学学院副教授,硕士生导师。分别于2009年和2014年在中山大学获得本科和博士学位。2014年至2016年在清华大学丘成桐数学科学中心担任博士后研究员,2016年起在中山大学数学学院工作。研究方向为几何分析。曾在流形上的调和函数, 正迷向曲率流形等方面的研究取得了一系列创新性研究成果。在J. Reine Angew. Math., Math. Ann.等国际著名数学期刊上发表多篇SCI论文。