22 research outputs found
Complete -submanifolds in Gauss spaces
In this paper, we study -submanifolds of arbitrary codimensions in
Gauss spaces. These submanifolds can be seen as natural generalizations of
self-shrinker and -hypersurfaces. Using a divergence type theorem and
some Simons' type identities, we prove some halfspace type theorems and gap
theorems for complete proper -submanifolds. These generalized our as
well as the others' results for self-shrinker or -hypersurfaces to
-submanifolds.Comment: 20 pages. All comments are welcom