【摘要】 主要研究欧氏空间中n维紧致子流形M上的一类质量泛函稳定流,证明了当M的截面曲率kM及其平均曲率向量长度‖H‖满足以下条件之一时,M上不存在稳定流:(1)kM>n82,(2)M是14-pinch子流形,‖H‖<;并部分地解决了L-S猜想.更多还原

【Abstract】 This paper studies the stable currents of a class of quality functional in a compact n-dimensional submanifold of Euclidean space.It is proved that there does not exist stable currents in M when its sectional curvature KM and the length of mean curvature ‖H‖ satisfy one of the following condtions:(1) KM>;(2) M is a 14-pinched submanifold with ‖H‖.We partialy answer the L-S conjecture.更多还原