ABSTRACT

We will discuss the mean curvature flow of n-dimensional submanifolds in $\mathbb{R}^{N}$ satisfying a pinching condition $|A|^2 < c|H|^2$ introduced by Andrews and Baker ('10). We will compare these flows to flows of hypersurfaces studied in the fundamental works of Huisken ('84) and Huisken-Sinestrari ('99, '09). Our primary goal is to discuss an estimate for these pinched flows which shows such flows must become nearly planar prior to singularity formation. At the end, we will discuss applications of the estimate to the study of singularity formation in the MCF in higher codimension.

BRIEF BIO

Keaton Naff is a fifth-year Ph.D student at Columbia University, working under the supervision of Prof. Simon Brendle. His interests lie in differential geometry and PDEs and, in particular, in the Ricci flow and mean curvature flow. His recent work is on singularities of the Ricci flow in higher dimension and the mean curvature flow in higher codimension.

ZOOM INFO

ID: 684 0711 9096
Password: 752374

https://zoom.com.cn/j/68407119096?pwd=NDZkdlNwK1pGdHR1a2pyd3U0ZUhzQT09

For more information about this seminar, please see below.

【Wednesday Online Seminar on Geometric Analysis】

This is the 22nd talk of Wednesday Online Seminar on Geometric Analysis, which is an online seminar organized by Prof. Gang Tian, Prof. Jie Qing, Prof. Zhenlei Zhang, and Prof. Xiaohua Zhu.

Below is a list of invited speakers:

April 8, 2020                  Wenshuai Jiang (Zhejiang University)

April 15, 2020                Chi Li (Purdue University)

April 22, 2020                Lu Wang (Caltech)

April 29, 2020                Jianchun Chu (Northwestern University)

May 6, 2020                  Richard Bamler (UC Berkeley)

May 13, 2020                Xin Zhou (UC Santa Barbara)

May 20, 2020                Daniel Stern (University of Toronto)

May 27, 2020                Jeff Streets (UC Irvine)

June 3, 2020                 Chenyang Xu (MIT)

June 10, 2020               Yi Lai (UC Berkeley)

June 17, 2020               Ben Andrews (Australian National University)

June 24, 2020               Shiguang Ma (Nankai University) 

July 1, 2020                   Yuchen Liu (Yale University)

July 7, 2020                   Min-Chun Hong (The University of Queensland)

July 15, 2020                 Jian Song (Rutgers University)

September 8, 2020        Martin Kerin (NUI Galway)

September 23, 2020      Richard Bamler (UC Berkeley) 

October 14, 2020           Chao Li (Princeton University)

October 21, 2020           Yu Yuan (University of Washington)

October 28, 2020           Aaron Naber (Northwestern University)

November 4, 2020         Carlo Scarpa (SISSA)

November 11, 2020       Keaton Naff (Columbia University)

December 9, 2020          Hans-Joachim Hein (Fordham University)

December 16, 2020        Lei Ni (UC San Diego)