Complete $$\lambda $$λ-hypersurfaces of weighted volume-preserving mean curvature flow

By Qing Cheng, G. Wei. 2014

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In this paper, we introduce a special class of hypersurfaces which are called $$\lambda $$λ-hypersurfaces related to a weighted volume preserving mean curvature flow in the Euclidean space. We prove that $$\lambda $$λ-hypersurfaces are critical points of the weighted area functional for the weighted volume-preserving variations. Furthermore, we classify complete $$\lambda $$λ-hypersurfaces with polynomial area growth and $$H-\lambda \ge 0$$H-λ≥0. The classification result generalizes the results of Huisken (J Differ Geom 31:285–299, 1990) and Colding and Minicozzi (Ann Math 175:755–833, 2012).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ef08bc38ec5baa133369cd34d61fb88b2b92b62b