On stable currents in positively pinched curved hypersurfaces

Jintang Li¹

¹Department of Mathematics Xiammen University 361005 Xiammen Fujian, P.R. China

Colloquium Mathematicum, Tome 98 (2003) no. 1, pp. 79-86

Résumé

Let $M^n\, (n\geq 3)$ be an $n$-dimensional complete hypersurface in a real space form $N(c)$ $(c\geq 0)$. We prove that if the sectional curvature $K_M$ of $M$ satisfies the following pinching condition: $c+\delta K_M\leq c+1,$ where $\delta ={1\over 5}$ for $n\geq 4$ and $\delta ={1\over 4}$ for $n=3$, then there are no stable currents (or stable varifolds) in $M$. This is a positive answer to the well-known conjecture of Lawson and Simons.

Détail

DOI : 10.4064/cm98-1-6

Keywords: geq n dimensional complete hypersurface real space form geq prove sectional curvature satisfies following pinching condition delta leq where delta geq delta there stable currents stable varifolds positive answer well known conjecture lawson simons