Complete $\lambda$-surfaces in ${\mathbb{R}}^3$

Abstract

The purpose of this paper is to study complete $\lambda$-surfaces in Euclidean space ${\mathbb{R}}^3$. A complete classification for 2-dimensional complete $\lambda$-surfaces in Euclidean space ${\mathbb{R}}^3$ with constant squared norm of the second fundamental form is given.

19 pages, comments are welcome

References in corpus (3)

• Complete $\lambda$-hypersurfaces of weighted volume-preserving mean curvature flow
• A new pinching theorem for complete self-shrinkers and its generalization
• Compact embedded $\lambda$-torus in Euclidean spaces

Cited by in corpus (1)

• A remark on a Bernstein type result for $\lambda$-hypersurfaces