The Rigidity Theorems of Self Shrinkers via Gauss maps
The Rigidity Theorems of Self Shrinkers via Gauss maps
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DOI：
10.1016/j.aim.2016.08.019
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发表时间：
2012-03
期刊：
影响因子：
--
通讯作者：
Q. Ding;Yuanlong Xin;Ling Yang
中科院分区：
文献类型：
--
作者：
Q. Ding;Yuanlong Xin;Ling Yang
通过对高斯映射下的象的限制，研究了欧氏空间中自收缩算子的刚性结果。目标流形的几何性质起作用。在自收缩超曲面情形下，定理3.1和定理3.2不仅改进了已有的结果，而且是最优的。在高余维情况下，利用高斯映射的目标流形（Grassmannian流形）的几何性质，给出了自缩图的刚性定理。
We study the rigidity results for self-shrinkers in Euclidean space by restriction of the image under the Gauss map. The geometric properties of the target manifolds carry into effect. In the self-shrinking hypersurface situation Theorem 3.1 and Theorem 3.2 not only improve the previous results, but also are optimal. In higher codimensional case, using geometric properties of the Grassmannian manifolds (the target manifolds of the Gauss map) we give a rigidity theorem for self-shrinking graphs.