Abstract
In this paper, we prove that any complete m-dimensional spacelike self-shrinkers in pseudo-Euclidean spaces Rnm+n must be affine planes, and there exists no complete m-dimensional spacelike translating soliton in Rnm+n. These results are proved by using a new Omori–Yau maximal principle. We also derive a rigidity theorem of self-shrinking hypersurfaces in Euclidean space with Gauss image lies in a regular ball.
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