Title: On Chen's conjecture for biharmonic hypersurfaces

Speaker：洪敏纯（澳大利亚昆士兰大学）

Place:管研楼1418

Time:16:00-17:00,May 11th

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 was settled in the case of $n=2$ by Chenand Jiang around 1987 independently.  Hasanis and Vlachos in 1995 settled Chen's conjecture for $n=3$. In collaboration with Fu and Zhan (Adv. Math. 2021), we  settled Chen's conjecture for hypersurfaces in $\mathbb R^{5}$ for  $n=4$. More recently, with Fu and Zhan , we find new techniques to settle Chen's conjecture on biharmonic hypersurfaces in $\Bbb R^6$ and the BMO  conjecture  on biharmonic hypersurfaces in $\mathbb S^6$.