一类质量泛函稳定流的不存在性定理

The Noexistence of Stable Current for a Class of Quality Functional

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.

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〉n^2‖H‖^2/8（n-1） ; （2） M is a 1/4-pinched submanifold with ‖H‖〈√2（n-1）/n .We partialy answer the L-S conjecture.