Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle
Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle
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DOI：
10.1007/s00526-015-0826-1
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发表时间：
2015-01
影响因子：
2.1
通讯作者：
Keita Kunikawa
中科院分区：
文献类型：
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作者：
Keita Kunikawa
我们给出了高维孤子平移完全图的伯恩斯坦型定理的证明。在超曲面的情况下，鲍石表明，其高斯图的图像包含在开放半球的紧子集中的平移孤子是超平面。这意味着不存在斜率有界的非平凡平移孤子。在本文中，我们将这个定理推广到任意余维。此外，我们获得了允许无限斜率的最佳生长条件。作为推论，我们的结果涵盖了最小子流形的经典伯恩斯坦型定理。
We give a proof for a Bernstein-type theorem of complete graphs of translating solitons in higher codimension. In the case of hypersurfaces, Bao–Shi showed that a translating soliton whose image of the Gauss map is contained in a compact subset in an open hemisphere is a hyperplane. This means that there is no nontrivial translating soliton whose slope is bounded. In the present article, we generalize this theorem in arbitrary codimension. Moreover we obtain an optimal growth condition which allows unbounded slopes. As a corollary, our result covers a classical Bernstein-type theorem for minimal submanifolds.