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.
|Number of pages||14|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2015 Oct 22|
ASJC Scopus subject areas
- Applied Mathematics