|
| 摘要: |
| 本文研究了self-shrinkers谱与几何的关系.利用渐进展开式系数相等的方法,获得了如下结果:设M是Rn+1上的n(n ≥ 2)维闭self-shrinkers,且M和Sn(√2n)有相同的平均曲率,如果specp(M)=specp(Sn(√2n)),则M是Sn(√2n),并推广了Rn+1上self-shrinkers的特征. |
| 关键词: self-shrinkers 平均曲率 谱 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:国家自然科学基金天元青年基金(11226078);拟爱因斯坦度量及相关问题(11261038). |
|
| ON SPECTRAL CHARACTERIZATIONS OF SELF-SHRINKERS ON Rn+1 |
|
HAN Fang-fang,YANG Deng-yun
|
| Abstract: |
| This article studies spectrum and geometric relations of self-shrinkers. By using the method of asymptotic expansion coefficient, we obtain the following results:Let M be an n-dismension closed self-shrinker on Rn+1(n ≥ 2) with the same mean curvature of Sn(√2n), if specp(M)=specp(Sn(√2n)) (p=0, 1, 2), then M is Sn(√2n), which generalizes the character of self-shrinkers on RN+1. |
| Key words: self-shrinkers mean curvature spectrum |
