Huisken proved that any hypersurface M<sub>0</sub> satisfying a suitable convexity conditionin a Riemannian manifold contracts to a simple point during the evolution along its meancurvature vector. In this...Huisken proved that any hypersurface M<sub>0</sub> satisfying a suitable convexity conditionin a Riemannian manifold contracts to a simple point during the evolution along its meancurvature vector. In this letter the author studies the evolution of hypersurfaces in a posi-tive pinched Einsteinnian manifold N<sup>n+1</sup> without assuming the convexity of initialhypersurface M<sub>0</sub> and obtains the same convergent result.展开更多
文摘Huisken proved that any hypersurface M<sub>0</sub> satisfying a suitable convexity conditionin a Riemannian manifold contracts to a simple point during the evolution along its meancurvature vector. In this letter the author studies the evolution of hypersurfaces in a posi-tive pinched Einsteinnian manifold N<sup>n+1</sup> without assuming the convexity of initialhypersurface M<sub>0</sub> and obtains the same convergent result.
