ABSTRACT

A longstanding conjecture on biharmonic submanifolds, proposed by Chen in 1991, is that any biharmonic submanifold in a Euclidean space is minimal. In the case of a hypersurface $M^n$ in $\mathbb R^{n+1}$, Chen's conjecture for a hypersurface was settled in the case of $n=2$ by Chen and Jiang in 1980’s, and by Hasanis and Vlachos in 1995 with $n=3$. However, the general Chen's conjecture on a hypersurface $M^n$ remains open for $n>3$. In this paper, we settle Chen's conjecture for hypersurfaces in $\mathbb R^{5}$ for $n=4$. This is my joint work with Yu Fu and Xin Zhan.

BRIEF BIO

Dr. Min-Chun Hong is currently an Associate Professor in the department of Mathematics at the University of Queensland, Australia. He received his Ph.D from Zhejiang University in China in 1988. His research interests lie primarily in geometric and nonlinear analysis. Hong has solved a number of open problems and conjectures on harmonic maps, liquid crystals and Yang Mills equations. Over these years, he has been collaborating with mathematicians such as Professor Mariano Giaquinta (SNS-Pisa), Professor Jurgen Jost (Germany), Professor Michael Struwe (Zurich), Professor Gang Tian (Princeton) and Professor Zhouping Xin (Hong Kong). For more details about him, please visit https://smp.uq.edu.au/profile/224/min-chun-hong.

ZOOM INFO

ID: 643 3205 4770

Password: 737061

SLIDES

You may find the slides here.

For more information about this seminar, please see below.

【Wednesday Online Seminar on Geometric Analysis】

This is the 14th 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)