Complete lambda-hypersurfaces of weighted volume-preserving mean curvature flow
Complete lambda-hypersurfaces of weighted volume-preserving mean curvature flow
复制标题
加权保体积平均曲率流的完整 lambda 超曲面
DOI：
10.1007/s00526-018-1303-4
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发表时间：
2018
影响因子：
2.1
通讯作者：
Wei Guoxin
中科院分区：
文献类型：
--
作者：
Cheng Qing-Ming;Wei Guoxin
本文在欧氏空间中引入一类特殊的超曲面，称之为与加权保体积平均曲率流相关的超曲面。我们证明了-超曲面是加权面积泛函的加权保体积变分的临界点。此外，我们还对多项式面积增长的完备超曲面进行了分类。分类结果概括了Huisken（J Differ Geom 31：285-299，1990）和Colding和Minicozzi（Ann Math 175：755-833，2012）的结果。
In this paper, we introduce a special class of hypersurfaces which are called-hypersurfaces related to a weighted volume preserving mean curvature flow in the Euclidean space. We prove that-hypersurfaces are critical points of the weighted area functional for the weighted volume-preserving variations. Furthermore, we classify complete-hypersurfaces with polynomial area growth and. The classification result generalizes the results of Huisken (J Differ Geom 31:285–299, 1990) and Colding and Minicozzi (Ann Math 175:755–833, 2012).